❚❘×❮◆● ✣❸■ ❍➴❈ ❆◆ ●■❆◆● ❑❍❖❆ ❙× P❍❸▼ ✣➋ ❚⑨■ ◆●❍■➊◆ ❈Ù❯ ❑❍❖❆ ❍➴❈ ❈❻P ❚❘×❮◆● ☎ ✣■➋❯ ❑■➏◆ ✣Õ ❈❍❖ ❚➑◆❍ ▲■➊◆ ❚Ö❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❚➮■ ×❯ ❱➹ ❚❍⑨◆❍ ❚⑨■ ❆◆ ●■❆◆●✱ ✵✼ ✲ ✷✵✶✽ ❚❘×❮◆● ✣❸■ ❍➴❈ ❆◆ ●■❆◆● ❑❍❖❆ ❙× P❍❸▼ ✣➋ ❚⑨■ ◆●❍■➊◆ ❈Ù❯ ❑❍❖❆ ❍➴❈ ❈❻P ❚❘×❮◆● ☎ ✣■➋❯ ❑■➏◆ ✣Õ ❈❍❖ ❚➑◆❍ ▲■➊◆ ❚Ö❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❚➮■ ×❯ ❱➹ ❚❍⑨◆❍ ❚⑨■ ❆◆ ●■❆◆●✱ ✵✼ ✲ ✷✵✶✽ ☎ ✣➲ t➔✐ ♥❣❤✐➯♥ ❝ù✉ ❦❤♦❛ ❤å❝ ✧✣■➋❯ ❑■➏◆ ✣Õ ❈❍❖ ❚➑◆❍ ▲■➊◆ ❚Ö❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❚➮■ ×❯✧ ❞♦ t→❝ ❣✐↔ ❱ã ❚❤➔♥❤ ❚➔✐✱ ❝æ♥❣ t→❝ t↕✐ ❇ë ♠ỉ♥ ❚♦→♥✱ ❑❤♦❛ ❙÷ ♣❤↕♠ t❤ü❝ ❤✐➺♥✳ ❚→❝ ❣✐↔ ✤➣ ❜→♦ ❝→♦ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ✈➔ ✤÷đ❝ ❍ë✐ ỗ t tổ q ✳ ✳ ✴✳ ✳ ✳ ✴✳ ✳ ✳ ✳ ✳ ữ ỵ P P t ỗ t ❝ù✉ ❦❤♦❛ ❤å❝ ✤÷đ❝ t❤ü❝ ❤✐➺♥ t↕✐ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❆♥ ●✐❛♥❣✳ ❚→❝ ❣✐↔ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ❝❤➙♥ t❤➔♥❤ ✤➳♥ ❇❛♥ ●✐→♠ ❤✐➺✉ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❆♥ ●✐❛♥❣✱ ❇❛♥ ❈❤õ ♥❤✐➺♠ ❑❤♦❛ ❙÷ ♣❤↕♠ ✈➔ ❝→❝ ❣✐↔♥❣ ✈✐➯♥ ❇ë ♠ỉ♥ ❚♦→♥ ✤➣ ❣✐ó♣ ✤ï✱ t↕♦ ✤✐➲✉ ❦✐➺♥ t❤✉➟♥ ❧ñ✐ ❝❤♦ t→❝ ❣✐↔ ❤♦➔♥ t❤➔♥❤ ✤➲ t➔✐ ♥❣❤✐➯♥ ❝ù✉ ♥➔②✳ ❚→❝ ❣✐↔ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ✤➳♥ P●❙✳ ❚❙✳ ▲➙♠ ◗✉è❝ ❆♥❤ ✈➔ ❚❙✳ ❚r➛♥ ◆❣å❝ ❚➙♠ ✈➻ ỳ qỵ tr q tr tỹ ✤➲ t➔✐✳ ❚→❝ ❣✐↔ ❝ơ♥❣ ①✐♥ ❣û✐ ❧í✐ ❝↔♠ ì♥ ❝❤➙♥ t❤➔♥❤ ✤➳♥ ❝→❝ t❤➔♥❤ ✈✐➯♥ tr♦♥❣ ♥❤â♠ s❡♠✐♥❛r tè✐ ÷✉ ❝õ❛ ❇ë ♠æ♥ ❚è✐ ÷✉ ✈➔ ❍➺ t❤è♥❣ ✲ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❑❤♦❛ ❤å❝ ❚ü ♥❤✐➯♥✱ ♥❤â♠ s❡♠✐♥❛r tè✐ ÷✉ ❝õ❛ ❇ë ♠ỉ♥ ❚♦→♥ ✲ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❈➛♥ ❚❤ì ✈➻ ♥❤ú♥❣ tr❛♦ ✤ê✐ ❤å❝ t❤✉➟t ❝â ❣✐→ trà ú t õ t ỵ tữ tr q tr➻♥❤ t❤ü❝ ❤✐➺♥ ✤➲ t➔✐✳ ❆♥ ❣✐❛♥❣✱ ♥❣➔② ✷✾ t❤→♥❣ ✵✼ ♥➠♠ ✷✵✶✽ ◆❣÷í✐ t❤ü❝ ❤✐➺♥ ❚❤❙✳ ❱ã ❚❤➔♥❤ ❚➔✐ ỵ tt tố ữ ♠ët ♥❤→♥❤ ❝õ❛ t♦→♥ ❤å❝ ✤÷đ❝ ♣❤→t tr✐➸♥ ✤➸ t➻♠ r❛ ♥❤ú♥❣ ❝→❝❤ tè✐ ÷✉ ✤➸ ✤✐➲✉ ❦❤✐➸♥ ♠ët ❤➺ t❤è♥❣ ✤ë♥❣ ❧ü❝✱ ♥â ❧➔ sü ♠ð rë♥❣ ❝õ❛ ♣❤➨♣ t➼♥❤ ❜✐➳♥ ♣❤➙♥✳ ❚r♦♥❣ t❤í✐ ❣✐❛♥ ❣➛♥ ✤➙②✱ ♠ët tr♦♥❣ ♥❤ú♥❣ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ✤÷đ❝ q✉❛♥ t➙♠ ❧➔ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ số ợ ữỡ tr tr t t t t ♥➔② ✤÷đ❝ ♥❤â♠ t→❝ ❣✐↔ ❇✳ ❚✳ ❑✐❡♥✱ ◆✳ ❚✳ ❚♦❛♥✱ ▼✳ ▼✳ ❲♦♥❣✱ ❏✳ ❈✳ ❨❛♦ ♥❣❤✐➯♥ ❝ù✉ ✈➔♦ tr õ sỹ tỗ t t ỷ tử ữợ t♦→♥ ✤÷đ❝ t❤✐➳t ❧➟♣✳ ❈❤♦ ✤➳♥ ♥❛②✱ ❝❤ó♥❣ tỉ✐ ♥❤➟♥ t❤➜② ❝❤÷❛ ❝â ❝ỉ♥❣ tr➻♥❤ ♥➔♦ ♥❣❤✐➯♥ ❝ù✉ t➼♥❤ ❧✐➯♥ tư❝ ❍☎ ♦❧❞❡r ❝❤♦ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ö t❤✉ë❝ t❤❛♠ sè ♥➔②✳ ▼ö❝ ✤➼❝❤ ❝õ❛ ✤➲ t➔✐ ❧➔ ♥❣❤✐➯♥ ❝ù✉ sü ê♥ ✤à♥❤ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ tố ữ tở t số ợ ữỡ tr➻♥❤ tr↕♥❣ t❤→✐ t✉②➳♥ t➼♥❤✳ ❈→❝ ✤✐➲✉ ❦✐➺♥ ✤õ ❝❤♦ t➼♥❤ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝❛❧♠ ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ ✤❛♥❣ ①➨t ✤÷đ❝ t❤✐➳t ❧➟♣✳ ◆❣♦➔✐ r❛✱ ✤➲ t➔✐ ❝ơ♥❣ tr➻♥❤ ❜➔② ù♥❣ ❞ư♥❣ ❝→❝ ❦➳t q✉↔ t ữủ trữớ ủ t ợ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉✳ ❚ø ✤â t❤➜② ✤÷đ❝ ❦➳t q✉↔ ❝õ❛ ✤➲ t➔✐ ❧➔ sü ♠ð rë♥❣ ❝❤♦ ❦➳t q trữợ õ õ t ũ rồ ✈➔ ❝ë♥❣ sü ❝❤♦ ❜➔✐ t♦→♥ ♥➔②✳ ❚ø ❦❤â❛✿ ❇➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉✱ sü ê♥ ✤à♥❤ ♥❣❤✐➺♠✱ t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝❛❧♠✳ ✐✐ ❆❇❙❚❘❆❈❚ ❖♣t✐♠❛❧ ❝♦♥tr♦❧ t❤❡♦r② ✐s ❛ ❜r❛♥❝❤ ♦❢ ♠❛t❤❡♠❛t✐❝s ❞❡✈❡❧♦♣❡❞ t♦ ❢✐♥❞ ♦♣t✐✲ ♠❛❧ ✇❛②s t♦ ❝♦♥tr♦❧ ❛ ❞②♥❛♠✐❝ s②st❡♠✱ ✇❤✐❝❤ ✐s ❛♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ❝❛❧❝✉❧✉s ♦❢ ✈❛r✐❛t✐♦♥s✳ ■♥ r❡❝❡♥t❧②✱ ♦♥❡ ♦❢ t❤❡ ♦♣t✐♠✐③❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥t❡r❡st❡❞ ✐♥ ✐s ❛ ♣❛r❛✲ ♠❡tr✐❝ ♦♣t✐♠❛❧ ❝♦♥tr♦❧ ♣r♦❜❧❡♠ ✇✐t❤ t❤❡ ❧✐♥❡❛r st❛t❡ ❡q✉❛t✐♦♥✳ ❚❤✐s ♣r♦❜❧❡♠ ✇❛s r❡s❡❛r❝❤❡❞ ❜② ❇✳ ❚✳ ❑✐❡♥✱ ◆✳ ❚✳ ❚♦❛♥✱ ▼✳ ▼✳ ❲♦♥❣ ❛♥❞ ❏✳ ❈✳ ❨❛♦ ✐♥ ✷✵✶✷✱ ✐♥ ✇❤✐❝❤ t❤❡ ❡①✐st❡♥❝❡ ♦❢ t❤❡ s♦❧✉t✐♦♥ ❛♥❞ t❤❡ ❧♦✇❡r s❡♠✐❝♦♥t✐♥✉✐t② ♦❢ t❤❡ s♦❧✉t✐♦♥ ♠❛♣ ♦❢ t❤❡ ♣r♦❜❧❡♠ ❛r❡ ❡st❛❜❧✐s❤❡❞✳ ❙♦ ❢❛r✱ ✇❡ ❤❛✈❡ ♥♦t ❢♦✉♥❞ ❛♥② ✇♦r❦ t♦ st✉❞② t❤❡ ❍☎♦❧❞❡r ❝♦♥t✐♥✉✐t② ♦❢ t❤✐s ♣❛r❛♠❡tr✐❝ ♦♣t✐♠❛❧ ❝♦♥tr♦❧ ♣r♦❜❧❡♠✳ ❚❤❡ ♣✉r♣♦s❡ ♦❢ t❤✐s ♣❛♣❡r ✐s t♦ st✉❞② t❤❡ st❛❜✐❧✐t② ♦❢ s♦❧✉t✐♦♥s t♦ ❛ ♣❛r❛♠❡t✲ r✐❝ ♦♣t✐♠❛❧ ❝♦♥tr♦❧ ♣r♦❜❧❡♠ ✇✐t❤ ❧✐♥❡❛r st❛t❡ ❡q✉❛t✐♦♥✳ ❙✉❢❢✐❝✐❡♥t ❝♦♥❞✐t✐♦♥s ❢♦r ❍☎♦❧❞❡r ❝❛❧♠ ❝♦♥t✐♥✉✐t② ♦❢ s♦❧✉t✐♦♥ ♠❛♣ t♦ t❤✐s ♣r♦❜❧❡♠ ❛r❡ ❡st❛❜❧✐s❤❡❞✳ ■♥ ❛❞✲ ❞✐t✐♦♥✱ t❤❡ ♣❛♣❡r ❛❧s♦ ♣r❡s❡♥ts ❛♥ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ♦❜t❛✐♥❡❞ r❡s✉❧ts t♦ ❛ ♣❛rt✐❝✉❧❛r ♣r♦❜❧❡♠ ❛s ✇❡❧❧✳ ❚❤❡ r❡s✉❧t ♦❢ t❤❡ ♣❛♣❡r ✐s t❤❡ ❡①t❡♥s✐♦♥ ♦❢ ♣r❡✈✐♦✉s r❡s✉❧ts ❜② t❤❡ ❣r♦✉♣ ♦❢ ❛✉t❤♦rs ❇✉✐ ❚r♦♥❣ ❑✐❡♥ ❡t ❛❧ ❢♦r t❤✐s ♣r♦❜❧❡♠✳ ❑❡②✇♦r❞s✿ ❖♣t✐♠❛❧ ❝♦♥tr♦❧ ♣r♦❜❧❡♠✱ s♦❧✉t✐♦♥ st❛❜✐❧✐t②✱ ❍☎♦❧❞❡r ❝❛❧♠ ❝♦♥t✐✲ ♥✉✐t②✳ ✐✐✐ ▲❮■ ❈❆▼ ❑➌❚ ❚æ✐ ①✐♥ ❝❛♠ ✤♦❛♥ ✤➙② ❧➔ ❝æ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ r✐➯♥❣ tæ✐✳ ❈→❝ sè ❧✐➺✉ tr♦♥❣ ❝æ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ❝â ①✉➜t ①ù rã r➔♥❣✳ ◆❤ú♥❣ ❦➳t ❧✉➟♥ ♠ỵ✐ ✈➲ ❦❤♦❛ ❤å❝ ❝õ❛ ❝ỉ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ♥➔② ❝❤÷❛ ✤÷đ❝ ❝ỉ♥❣ ❜è tr♦♥❣ ❜➜t ❦ý ❝æ♥❣ tr➻♥❤ ♥➔♦ ❦❤→❝✳ ❆♥ ●✐❛♥❣✱ ♥❣➔② ✷✾ t❤→♥❣ ✵✼ ♥➠♠ ✷✵✶✽ ◆❣÷í✐ t❤ü❝ ❤✐➺♥ ❚❤❙✳ ❱ã ❚❤➔♥❤ ❚➔✐ ✐✈ ▼Ư❈ ▲Ư❈ ❈❤÷ì♥❣ ✶✳ ❚✃◆● ◗❯❆◆ ❱❻◆ ✣➋ ◆●❍■➊◆ ❈Ù❯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✶✳ ❚ê♥❣ q✉❛♥ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✷✳ ❚ê♥❣ q✉❛♥ ❜➔✐ t♦→♥ ❝➙♥ ❜➡♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ❈❤÷ì♥❣ ✷✳ ❑■➌◆ ❚❍Ù❈ ❈❍❯❽◆ ❇➚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✶✳ P❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❝õ❛ →♥❤ ①↕ ✤❛ trà ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✶✳ ⑩♥❤ ①↕ ✤❛ trà ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✷✳ ❚➼♥❤ ♥û❛ tử tr t ỷ tử ữợ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ ❧✐➯♥ q✉❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✷✳✹✳ ❚➼♥❤ ✤ì♥ ✤✐➺✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✷✳✷✳✺✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ☎ ❈❤÷ì♥❣ ✸✳ ❚➑◆❍ ▲■➊◆ ❚Ö❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❚➮■ ×❯ P❍Ư ❚❍❯❐❈ ❚❍❆▼ ❙➮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✸✳✶✳ ▼æ ❤➻♥❤ ❜➔✐ t♦→♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỷ tử ữợ ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✸✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✹✳ ⑩♣ ❞ö♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ☎ ❈❤÷ì♥❣ ✹✳ ❚➑◆❍ ▲■➊◆ ❚Ư❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❈❹◆ ❇➀◆● P❍Ö ❚❍❯❐❈ ❚❍❆▼ ❙➮ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶✳ ❇➔✐ t♦→♥ ❝➙♥ ổ ữợ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶✳✶✳ ▼æ ❤➻♥❤ ❜➔✐ t♦→♥ ❝➙♥ ❜➡♥❣ ổ ữợ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶✳✷✳ ▼ët sè tr÷í♥❣ ❤đ♣ ✤➦❝ ❜✐➺t ❝õ❛ ❜➔✐ t♦→♥ ❝➙♥ ❜➡♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✶✳✸✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❝❤➼♥❤ ①→❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷✳ ❇➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷✳✶✳ ▼æ ❤➻♥❤ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè ✳ ✳ ✳ ✷✾ ✈ ✹✳✷✳✷✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✷✳✸✳ ⑩♣ ❞ö♥❣ ✈➔♦ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ t❤❛♠ sè ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ❚➔✐ ❧✐➺✉ t❤❛♠ ❦❤↔♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✈✐ ▼Ð ✣❺❯ ✶ ❇➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ❚r♦♥❣ t❤ü❝ t✐➵♥ ❝✉ë❝ sè♥❣✱ ♥❤✐➲✉ ❜➔✐ t♦→♥ ✤➲ ❝➟♣ ✤➳♥ ❝→❝ ✈➜♥ ✤➲ ❦ÿ t❤✉➟t ✈➔ ✤✐➲✉ ❦❤✐➸♥ t❤÷í♥❣ ❧✐➯♥ q✉❛♥ ✤➳♥ ❝→❝ ❤➺ ✤ë♥❣ ❧ü❝ ✤÷đ❝ ♠ỉ t↔ ❜➡♥❣ ❝→❝ ♣❤÷ì♥❣ tr➻♥❤ t♦→♥ ❤å❝ ❞↕♥❣ x(t) ˙ = f (t, x(t), u(t)), t ≥ 0, tr♦♥❣ ✤â x(t) ❧➔ ❜✐➳♥ tr↕♥❣ t❤→✐ ♠æ t↔ ✤è✐ t÷đ♥❣ ✤➛✉ r❛ ✈➔ u(t) ❧➔ ❜✐➳♥ ✤✐➲✉ ❦❤✐➸♥ ♠ỉ t↔ ✤è✐ t÷đ♥❣ ✤➛✉ ✈➔♦✱ ♥❤ú♥❣ ❞ú ❧✐➺✉ ✤➛✉ ✈➔♦ ❝â t→❝ ✤ë♥❣ q✉❛♥ trå♥❣ ❝â t❤➸ ❧➔♠ ↔♥❤ ❤÷ð♥❣ ✤➳♥ sü ✈➟♥ ❤➔♥❤ ✤➛✉ r❛ ❝õ❛ ❤➺ t❤è♥❣✳ ▼ö❝ ✤➼❝❤ ❝❤➼♥❤ ❝õ❛ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❤➺ t❤è♥❣ ❧➔ t➻♠ ❝→❝❤ ✤✐➲✉ ❦❤✐➸♥ ✤➛✉ ✈➔♦ s❛♦ ❝❤♦ ✤➛✉ r❛ ❝â ♥❤ú♥❣ t➼♥❤ ❝❤➜t ♠➔ t❛ ♠♦♥❣ ♠✉è♥✳ ❉♦ ✤â ♥↔② s✐♥❤ ✈➜♥ ✤➲ t❤÷í♥❣ ❣➦♣ tr♦♥❣ ❝→❝ ❜➔✐ t♦→♥ t❤ü❝ t➳ ❧➔ ❧➔♠ t❤➳ ♥➔♦ ✤➸ ❝❤å♥ r❛ ởt ữỡ tố ữ ợ tố ♠æ t↔ q✉→ tr➻♥❤ s↔♥ ①✉➜t s↔♥ ♣❤➞♠ tr♦♥❣ ❜➔✐ t♦→♥ ❦✐♥❤ t➳✱ ❜➡♥❣ ❝→❝❤ t➻♠ ❝→❝ ❞ú ❦✐➺♥ ✤✐➲✉ ❦❤✐➸♥ ✭♥❤÷ ❣✐→ t❤➔♥❤ s↔♥ ♣❤➞♠✱ tè❝ ✤ë s↔♥ ①✉➜t ♠ët ✤ì♥ ✈à s↔♥ ♣❤➞♠ tr♦♥❣ ♠ët ✤ì♥ ✈à t❤í✐ ❣✐❛♥✱✳ ✳ ✳ ✮ ♥❣÷í✐ t❛ ❝â t❤➸ ✤✐➲✉ ❦❤✐➸♥ q✉→ tr➻♥❤ s↔♥ ①✉➜t s❛♦ ❝❤♦ s↔♥ ♣❤➞♠ s↔♥ ①✉➜t r❛ ✤↕t ✤÷đ❝ ❝❤➜t ❧÷đ♥❣ tèt ♥❤➜t ❤♦➦❝ ❝❤✐ ♣❤➼ ❣✐→ t❤➔♥❤ ♥❤ä ♥❤➜t✱✳ ✳ ✳ ❚❛ ❜➢t ✤➛✉ tø ❜➔✐ t♦→♥ ❜✐➳♥ ♣❤➙♥ ❝ê ✤✐➸♥ ❝õ❛ ▲❛❣r❛♥❣❡✿ ❳➨t ❧ỵ♣ ❤➔♠ ❧✐➯♥ tö❝ t✉②➺t ✤è✐ x(t) : [t0 , t1 ] → Rn ✈ỵ✐ ❝→❝ ✤✐➲✉ ❦✐➺♥ ❜✐➯♥ x(t0 ) = x0 , x(t1 ) = x1 ❱➜♥ ✤➲ ✤➦t r❛ ❧➔ t➻♠ ♠ët ❤➔♠ x(t) s❛♦ ❝❤♦ ❤➔♠ ♠ö❝ t✐➯✉ t1 J(x) = g(t, x(t), x(t))dt, ˙ t0 ✤↕t ❣✐→ trà tè✐ t❤✐➸✉✳ ◆➳✉ t❛ ✤÷❛ ✈➔♦ ①➨t ❤➺ ✤✐➲✉ ❦❤✐➸♥ x(t) ˙ = u(t), t ∈ [t0 , t1 ], x(t0 ) = x0 , x(t1 ) = x1 , ✈➔ ❤➔♠ ♠ö❝ t✐➯✉ t1 J(u) = g(t, x(t), u(t))dt, t0 t❤➻ ❜➔✐ t♦→♥ ❜✐➳♥ ♣❤➙♥ ❝ê ✤✐➸♥ s➩ ✤÷đ❝ ✤÷❛ ✈➲ ❜➔✐ t♦→♥ tè✐ ÷✉ ❤➔♠ ♠ö❝ t✐➯✉ J(u) tr➯♥ ❝→❝ t➟♣ ✤✐➲✉ ❦❤✐➸♥ ❝❤➜♣ ♥❤➟♥ ✤÷đ❝ u(t) ❝❤♦ ♣❤÷ì♥❣ tr➻♥❤ ✤✐➲✉ ❦❤✐➸♥ x(t) ˙ = u(t)✳ ◆❤÷ ✈➟②✱ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ s➩ ❝â ❜è♥ ✤è✐ t÷đ♥❣ ♥❣❤✐➯♥ ❝ù✉ ❝❤➼♥❤ s❛✉✿ ✐✳ ❍➺ t❤è♥❣ ✤✐➲✉ ❦❤✐➸♥ ♠ỉ t↔ q✉→ tr➻♥❤ ❝❤✉②➸♥ ✤ë♥❣ t÷ì♥❣ q✉❛♥ ❣✐ú❛ ✤➛✉ ✈➔♦ ✭✤✐➲✉ ❦❤✐➸♥ u(t)✮ ✈➔ ✤➛✉ r❛ ✭tr↕♥❣ t❤→✐ x(t)✮✳ ◗✉→ tr➻♥❤ ♥➔② t❤÷í♥❣ ✤÷đ❝ ❝❤♦ ❜ð✐ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ ❞↕♥❣ x(t) ˙ = f (t, x(t), u(t)), t ỵ ữủ ự S ỷ tử ữợ t↕✐ (¯ µ, λ) ❱➼ ❞ư ✸✳✶✳ ✭❑✐❡♥✱ ❚♦❛♥✱ ❲♦♥❣ ✈➔ ❨❛♦✱ ✷✵✶✷✱ ❱➼ ❞ö ✸✳✶✮ ●✐↔ sû r➡♥❣ n = 2, m = ¯ = (0, 0)✳ ❱ỵ✐ ♠é✐ (µ, λ) ∈ B ¯M (¯ 1, k = l = 1, p = ✈➔ (¯ µ, λ) µ, 1) ì , t t à2 J(x, u, µ) = (µ(t)(x (t) + x (t) + u (t) + dt → inf, µ + u2 (t) x˙ = x1 + tu + λ1 , P (µ, λ) x˙ = x + u + λ , 2 x1 (0) = x2 (0) = 1, u ∈ [−1, 1], t ∈ [0, 1] h.k.n ❑❤✐ ✤â✱ t❛ ❝â ❝→❝ ✤✐➲✉ ❦❤➥♥❣ ✤à♥❤ s❛✉ ✤➙②✿ ✭❛✮ P (µ, λ) ❝â ❞✉② ♥❤➜t ♥❣❤✐➺♠ (¯ x, u¯) = (exp t, exp t, 0); ✭❜✮ J(x, u, µ) t❤♦↔ ♠➣♥ ❝→❝ ✤✐➲✉ ❦✐➺♥ (A1 ) − (A5 ) ỵ ệ ế ỵ sỷ r ỗ t số ữỡ T1 , T2 ✈➔ ♠ët ❤➔♠ ❦❤æ♥❣ ➙♠ φ ∈ Lp ([0, 1], Rm ) s❛♦ ❝❤♦ |A(t)| ≤ T1 , |T (t)| ≤ T2 , |B(t)| ≤ φ(t) t ∈ [0, 1] ; s ợ V f (Ã, tỗ t ởt ❝➟♥ V ❝õ❛ µ ¯ ✈➔ N ❝õ❛ λ ¯) t h à ỗ tử m · δ ✲❍☎♦❧❞❡r tr➯♥ K(N )❀ ✭✐✐✐✮ ✈ỵ✐ ♠é✐ z ∈ K(N ), f (z, ·) ❧➔ n · γ ✲❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ µ ¯✳ ¯ µ ❑❤✐ ✤â✱ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❖❈P✮ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ (λ, ¯ )✳ ❈❤ù♥❣ ♠✐♥❤✳ ❈❤ó♥❣ t❛ ❝❤✐❛ ❝❤ù♥❣ t ữợ ữợ ợ t ự K() t ỗ õ ré♥❣✳ ❱➔ t❛ ❝❤➾ r❛ r➡♥❣ ✈ỵ✐ λ1 , λ2 trữợ ợ z1 = (x1 , u1 ) K(1 ) ổ tỗ t z2 = (x2 , u2 ) ∈ K(λ2 ) ✈➔ ♠ët ❤➡♥❣ sè l s❛♦ ❝❤♦ z1 − z2 ) ≤ l λ1 − λ2 r ✭✸✳✶✵✮ ❚❤➟t ✈➟②✱ t❤❡♦ ✤à♥❤ ỵ tỗ t ữỡ tr t t➼♥❤ t❤➻ K(λ) = ∅ ✈ỵ✐ ♠å✐ λ ∈ Λ ✷✵ ▼➦t ❦❤→❝✱ ✈ỵ✐ ♠å✐ z1 , z2 ∈ K(λ), z1 = (x1 , u1 ), z2 = (x2 , u2 )✱ ✈ỵ✐ ♠å✐ θ ∈ (0, 1), t❛ ❝â θx˙ + (1 − θ)x˙ = θA(t)x1 (t) + θB(t)u1 (t) + θT (t)λ(t) +(1 − θ)A(t)x2 (t) + (1 − θ)B(t)u2 (t) + (1 − θ)T (t)λ(t) = A(t)(θx1 + (1 − θ)x2 ) + B(t)(θu1 + (1 − θ)u2 ) + T (t)λ(t) ❙✉② r❛ θz1 + (1 − θ)z2 ∈ K(λ) ❉♦ ✤â K(λ) ❧➔ t ỗ r zi = (xi , ui ) ∈ K(λ) s❛♦ ❝❤♦ zi → z = (x, u)✳ ❑❤✐ ✤â xi → x, x˙i → x˙ ✈➔ ui → u tr♦♥❣ L1 ✈ỵ✐ ♠å✐ t ∈ [0; 1] ❤➛✉ ❦❤➢♣ ♥ì✐✳ ❑❤✐ ✤â t❛ ❝â x˙ (t) = A(t)x (t) + B(t)u (t) + T (t)λ(t), i i i xi (0) = x0 ❈❤♦ i → ∞ t❛ t❤✉ ✤÷đ❝ x(t) ˙ = A(t)x(t) + B(t)u(t) + T (t)λ(t), x(0) = x0 ✭✸✳✶✶✮ ✭✸✳✶✷✮ ◆❣♦➔✐ r❛✱ t❛ ❝â u(t) ∈ U ✈ỵ✐ ♠å✐ t ∈ [0; 1] ❤➛✉ ❦❤➢♣ ♥ì✐✳ ❙✉② r❛ z ∈ K(λ)✳ ❉♦ ✤â✱ K(λ) ❧➔ t➟♣ ✤â♥❣✳ ❇➙② ❣✐í t❛ ❝❤➾ r r ợ , trữợ ✈ỵ✐ ♠å✐ z1 = (x1 , u1 ) ∈ K(λ1 ) ổ tỗ t z2 = (x2 , u2 ) ∈ K(λ2 ) ✈➔ ♠ët ❤➡♥❣ sè l s❛♦ ❝❤♦ z1 − z2 ) ≤ l λ1 − λ2 r ❚❤➟t ✈➟②✱ ✈ỵ✐ ♠å✐ (x1 , u1 ) ∈ K(λ1 ) t❤➻ x˙1 = A(t)x1 (t) + B(t)u1 (t) + T (t)λ1 (t), t ∈ [0, 1] ❤✳❦✳♥ ✭✸✳✶✸✮ u2 = u1 ỵ tỗ t ♥❣❤✐➺♠ ❝❤♦ ❜➔✐ t♦→♥ ❈❛✉❝❤② ❝õ❛ ♣❤÷ì♥❣ tr➻♥❤ ✈✐ ♣❤➙♥ t t tỗ t x2 X s x2 = A(t)x2 (t) + B(t)u2 (t) + T (t)λ2 (t), t ∈ [0, 1] ❤✳❦✳♥ ❚rø ✭✸✳✶✸✮ ❝❤♦ ✭✸✳✶✹✮ ✈➔ ✤➦t x = x1 − x2 ✱ t❛ ❝â x(0) = ✈➔ x˙ = A(t)x(t) + T (t)(λ1 (t) − λ2 (t)), t ∈ [0, 1] ❤✳❦✳♥ ✷✶ ✭✸✳✶✹✮ ❙✉② r❛ |x| ˙ ≤ T1 |x(t)| + T2 |λ1 (t) − λ2 (t)|, t ∈ [0, 1] ❤✳❦✳♥ ❚ø x(t) = t ✭✸✳✶✺✮ x(s)ds ˙ ✱ t❛ ✤÷đ❝ t |x(t)| ≤ (T1 |x(s)| + T2 |λ1 (s) − λ2 (s)|)ds t ≤ T1 |x(s)|ds + T2 |λ1 (t) − λ2 (t)|dt t ≤ T1 |x(s)|ds + T2 |λ1 − λ2 |1 t ≤ T1 |x(s)|ds + T2 |λ1 − λ2 |r ❚❤❡♦ ❜➜t ✤➥♥❣ t❤ù❝ ●r♦♥✇❛❧❧✱ t❛ ✤÷đ❝ t ¯ − λ|r exp( |x(t)| ≤ T2 |λ T1 ds) ≤ T2 λ1 − λ2 r exp(T1 ) r = l λ1 − λ2 r , ❑➳t ❤đ♣ ✈ỵ✐ ✭✸✳✶✺✮✱ t❛ ❝â x(t) ˙ ≤ T1 x + T2 λ1 − λ2 ≤ T1 (T2 λ1 − λ2 r r exp(T1 )) + T2 λ1 − λ2 tr♦♥❣ ✤â l := T1 T2 exp(T1 ) + T2 ✳ ❉♦ ✤â✱ t❛ ❝â z1 −z2 = (x1 , u1 )−(x2 , u2 ) = x1 −x2 1,1 = x 1,1 = |x(0)|+ x˙ ≤ l λ1 −λ2 r ữợ ợ z0 S(, ) z ∈ S(λ, µ)✱ t❛ ❝➛♥ ❝❤ù♥❣ ♠✐♥❤ d(z0 , z) ≤ 2n h 1/β dγ/β (µ, µ ¯) ✭✸✳✶✻✮ ❉➵ t❤➜② ✭✸✳✶✻✮ ✤ó♥❣ ♥➳✉ z0 = z ✳ ●✐↔ sû r➡♥❣ z0 = z ✳ ❚ø z0 ∈ S(λ, µ ¯) ✈➔ z ∈ S(λ, µ) ✱ t❛ ❝â✿ f (w1 , µ ¯) − f (z0 , µ ¯) ≥ 0, ∀w1 ∈ K(λ), ✷✷ ✭✸✳✶✼✮ ✭✸✳✶✽✮ f (w2 , µ) − f (z, µ) ≥ 0, ∀w2 K() t ỗ K() t õ ❝â✿ f z0 +z ∈ K(λ) ✣➦t w1 = z0 +z tr♦♥❣ ✭✸✳✶✼✮✱ t❛ z0 + z ,µ ¯ − f (z0 , µ ¯) ≥ t t ỗ f t❛ ❝â✿ f z0 + z ,µ ¯ 1 ≤ f (z0 , µ ¯) + f (z, µ ¯) − hdβ (z0 , z) 2 ❙✉② r❛ β hd (z0 , z) + f z0 + z 1 ,µ ¯ − f (z0 , µ ¯) ≤ − f (z0 , µ ¯) + f (z, µ ¯) 2 ✭✸✳✷✵✮ ❑➳t ❤đ♣ ✭✸✳✷✵✮ ✈ỵ✐ ✭✸✳✶✾✮ t❛ ❝â✿ β hd (z0 , z) ≤ f (z, µ ¯) − f (z0 , µ ¯) ❇➙② ❣✐í✱ ✤➦t w2 = z0 +z ✭✸✳✷✶✮ ✐♥ ✭✸✳✶✽✮ t❛ ✤÷đ❝✿ z0 + z , µ − f (z, µ) ≥ f t ỗ f t❛ ❝â f z0 + z ,µ 1 ≤ f (z0 , µ) + f (z, µ) − hdβ (z0 , z) 2 ❙✉② r❛ β hd (z0 , z) + f z0 + z 1 , µ − f (z0 , µ) ≤ − f (z0 , µ) + f (z, µ) 2 ✭✸✳✷✸✮ ❑➳t ❤đ♣ ✭✸✳✷✸✮ ✈ỵ✐ ✭✸✳✷✷✮ t❛ ✤÷đ❝✿ β hd (z0 , z) ≤ f (z0 , µ) − f (z, µ) ❚ø ✭✸✳✷✶✮ ✈➔ ✭✸✳✷✹✮ s✉② r❛ hdβ (z0 , z) ≤ (f (z, µ ¯) − f (z, µ)) + (f (z0 , µ) − f (z0 , µ ¯)), ❙û ❞ư♥❣ t➼♥❤ ❍♦❧❞❡r ❝❛❧♠ ❝õ❛ f t↕✐ µ ¯ tr♦♥❣ ✭✐✐✐✮ t ữủ hd (z0 , z) 2nd (à, ¯) ✷✸ ✭✸✳✷✹✮ ❉♦ ✤â ✭✸✳✶✻✮ ✤÷đ❝ ❝❤ù♥❣ ♠✐♥❤✳ ¯ ữợ t ự r ợ ♠å✐ z¯ ∈ S(λ, ¯) ✈➔ z0 ∈ S(λ, µ ¯) t❤➻ d(z0 , z¯) ≤ 1/β 4m21−δ lδ h ¯ dδ/β (λ, λ) ✭✸✳✷✺✮ ❉➵ t❤➜② ✭✸✳✷✺✮ ✤ó♥❣ ♥➳✉ z0 = z¯✳ ¯ s❛♦ ❝❤♦ ●✐↔ sû z0 = z tỗ t z1 K(), z2 K(λ) ¯ d(¯ z , z1 ) ≤ ld(λ, λ); ✭✸✳✷✻✮ ¯ d(z0 , z2 ) ≤ ld(λ, λ) ✭✸✳✷✼✮ ❉♦ z¯ ✈➔ z0 ❧➔ ♥❣❤✐➺♠ ❝õ❛ ✭❖❈P✮ ♥➯♥ t❛ ❝â✿ f (z2 , µ ¯) − f (¯ z, µ ¯) ≥ 0; ✭✸✳✷✽✮ f (z1 , µ ¯) − f (z0 , µ ¯) ≥ ✭✸✳✷✾✮ ✈➔ t t ỗ K() f z¯+z2 ¯ ✳ ❑❤✐ ✤â✱ t❤❡♦ ✭✸✳✷✽✮ t❛ ❝â ∈ K(λ) z¯ + z2 ,µ ¯ − f (¯ z, µ ¯) ≥ 0; ✭✸✳✸✵✮ ◆❣♦➔✐ r❛✱ ❞♦ t ỗ f 1 hd (z0 , z¯) ≤ f (z0 , µ ¯) + f (¯ z, µ ¯) − f 2 z0 + z¯ ,µ ¯ ✭✸✳✸✶✮ ❈ë♥❣ ✭✸✳✸✵✮ ✈➔ ✭✸✳✸✶✮✱ t❛ ❝â 1 β hd (z0 , z¯) ≤ f (z0 , µ ¯) − f (¯ z, µ ¯) + f 2 ◆❤➙♥ ✭✸✳✷✾✮ ✇✐t❤ z¯ + z2 ,µ ¯ −f z0 + z¯ ,µ ¯ ✭✸✳✸✷✮ ợ t ữủ 1 hd (z0 , z¯) ≤ f (z1 , µ ¯) − f (¯ z, µ ¯) + f 2 z¯ + z2 ,µ ¯ −f z0 + z¯ ), µ ¯ ▼➦t ❦❤→❝✱ ❞♦ t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝❛❧♠ ❝õ❛ f ♥➯♥ β δ z¯ + z2 z0 + z¯ hd (z0 , z¯) ≤ md (z1 , z¯) + mdδ , 2 δ δ ≤ md (z1 , z¯) + δ md (z2 , z¯) 2 t ủ ợ t ữủ β ¯ hd (z0 , z¯) ≤ m21−δ lδ dδ (λ, λ), ❙✉② r❛ d(z0 , z¯) ≤ 4m21−δ l h 1/ d/ (, ) ữợ ✹✳ ❚❛ t❤➜② r➡♥❣✱ ✈ỵ✐ ♠å✐ z¯ ∈ S(λ, ¯) ✈➔ z ∈ S(λ, µ)✱ d(¯ z , z) ≤ d(¯ z , z0 ) + d(z0 , z) ≤ 4m21−δ lδ h 1/β δ/β d ¯ + (λ, λ) 2n h 1/β dγ/β (µ, µ ¯) ✳ ❉♦ ✤â✱ ¯ µ ρ(S(λ, ¯), S(λ, µ)) ≤ 4m21−δ lδ h 1/β ¯ + dδ/β (λ, λ) 2n h 1/β dγ/β (µ, µ ¯) ¯ µ ❱➟② S ❧✐➯♥ tư❝ ❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ (λ, ¯)✳ ✸✳✹ ⑩P ❉Ö◆● ❚r♦♥❣ ♣❤➛♥ ♥➔②✱ t❛ →♣ ❞ö♥❣ ❦➳t q✉↔ ❝õ❛ ▼ö❝ ✸✳✸ ✈➔♦ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè ợ ữỡ tr tr t t t ữủ t tr ❜➔✐ ❜→♦ ❝õ❛ ♥❤â♠ t→❝ ❣✐↔ ❇ò✐ ❚rå♥❣ ❑✐➯♥ ✈➔ ❝ë♥❣ sü ✭❑✐❡♥ ✈➔ ❝s✳✱ ✷✵✶✷✮ ✤➸ t❤➜② ✤÷đ❝ ❦➳t q t ữủ ợ ỡ t ỷ tử ữợ u Lp ([0, 1] , Rm ) , < p < ∞ ✈➔ ❤➔♠ x ∈ W 1,1 ([0, 1] , Rn ) s❛♦ ❝❤♦ ❝ü❝ t✐➸✉ ❣✐→ trà g (x (t) , u (t) , µ (t)) dt, ợ ữỡ tr tr t x = A (t) x (t) + B (t) u (t) + T (t) λ (t) , t ∈ [0, 1] ❤✳❦✳♥✱ ✭✸✳✸✹✮ ❣✐→ trà ❜❛♥ ✤➛✉ x (0) = x0 , ✭✸✳✸✺✮ u (t) ∈ U, t ∈ [0, 1] ✭✸✳✸✻✮ ợ (, à) × M, t❛ ✤➦t 1 g (x (t) , u (t) , µ (t)) dt = f (z, µ) = g (z (t) , µ (t)) dt ❑❤✐ ✤â ❜➔✐ t♦→♥ tr➯♥ trð t❤➔♥❤ ✭❖❈P✶✮✿ f (z, µ) z∈K(λ) ❍➺ q✉↔ ✸✳✶✳ ●✐↔ sû r➡♥❣✱ tỗ t số ữỡ T1 , T2 ✈➔ ♠ët ❤➔♠ ❦❤æ♥❣ ➙♠ φ ∈ Lp ([0, 1] , Rm ) s❛♦ ❝❤♦ |A (t)| T1 , |T (t)| T2 , |B (t)| φ (t) , t ∈ [0, 1] s ợ V, g (Ã, à) tỗ t ❝➟♥ V ❝õ❛ µ ¯ ✈➔ N ❝õ❛ λ h1 ỗ m1 r tr K (N ) ; ✭❝✮ ✈ỵ✐ ♠é✐ z ∈ K (N ) , g (z, ·) ❧➔ n1 γ1 ✲❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ µ ¯✳ ¯ µ ¯ ❑❤✐ ✤â✱ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❖❈P✶✮ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ λ, ❈❤ù♥❣ ♠✐♥❤✳ ❚❛ ❝❤ù♥❣ ♠✐♥❤ ❤➺ q✉↔ ♥➔② ❜➡♥❣ tr tt ỵ ❚❛ t❤➜② r➡♥❣ ❣✐↔ t❤✐➳t ✭✐✮ ❤✐➸♥ ♥❤✐➯♥ ✤÷đ❝ t❤♦↔ ♠➣♥✳ ❱ỵ✐ ❣✐↔ t❤✐➳t ✭✐✐✮✱ t❤❡♦ ❣✐↔ t❤✐➳t ✭❜✮ ✈➲ t h1 ỗ g (Ã, à) ✈ỵ✐ ♠å✐ z1 , z2 ∈ K (N ) , θ ∈ [0, 1] t❛ ❝â g (θz1 + (1 − θ) z2 , µ) dt f (θz1 + (1 − θ)z2 , µ) = 1 g (z2 , µ) dt − h1 θ (1 − θ) dβ1 (z1 , z2 ) g (z1 , µ) dt + (1 − θ) θ 0 θf (z1 , µ) + (1 − θ) f (z2 , µ) − h1 θ (1 − θ) dβ1 (z1 , z2 ) õ t ỗ f (Ã, µ) tr➯♥ K (N ) tr♦♥❣ ✭✐✐✮ ✤÷đ❝ t❤ä❛ ♠➣♥✳ ▼➦t ❦❤→❝✱ ✈ỵ✐ ♠å✐ z1 , z2 ∈ K (N ) t❛ ❝â |f (z1 , µ) − f (z2 , µ)| = g (z1 , µ) dt − g (z2 , µ) dt (g (z1 , µ) − g (z2 , µ)) dt = |g (z1 , µ) − g (z2 , µ)| dt m1 dδ1 (z1 , z2 ) dt = m1 dδ1 (z1 , z2 ) ✷✻ ✣✐➲✉ ♥➔② ✤ó♥❣ ❞♦ t➼♥❤ ❧✐➯♥ tư❝ ❍☎♦❧❞❡r ❝õ❛ g ◆❤÷ ✈➟②✱ t➼♥❤ ❧✐➯♥ tư❝ ❍☎ ♦❧❞❡r ❝õ❛ f tr ữủ t ợ tt ❞➔♥❣ ✤÷đ❝ s✉② r❛ ❞ü❛ ✈➔♦ ❣✐↔ t❤✐➳t ✭❝✮ ✈➲ t➼♥❤ ❍☎ ♦❧❞❡r ❝❛❧♠ ❝õ❛ ❤➔♠ g ✳ ¯ µ ❱➟② →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❖❈P✶✮ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝❛❧♠ t↕✐ λ, ¯ ✷✼ ❈❍×❒◆● ✹✳ ☎ ❚➑◆❍ ▲■➊◆ ❚Ö❈ ❍❖▲❉❊❘ ❈Õ❆ ⑩◆❍ ❳❸ ◆●❍■➏▼ ❇⑨■ ❚❖⑩◆ ✣■➋❯ Pệ ữỡ ợ t t ổ ữợ t tử ❍☎ ♦❧❞❡r ❝õ❛ ❜➔✐ t♦→♥ ♥➔②✳ ❙❛✉ ✤â ♠ð rë♥❣ ♥❣❤✐➯♥ ❝ù✉ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè✱ ❣✐ỵ✐ t❤✐➺✉ t➼♥❤ ❧✐➯♥ tư❝ ❍☎♦❧❞❡r ❝õ❛ ❜➔✐ t♦→♥ ✈➔ →♣ ❞ư♥❣ ✈➔♦ tr÷í♥❣ ❤đ♣ ❝ư t❤➸ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè✳ ✹✳✶ ❇⑨■ ❚❖⑩◆ ❈❹◆ ❇➀◆● ❱➷ ❍×❰◆● ✹✳✶✳✶ ▼ỉ ❤➻♥❤ ❜➔✐ t ổ ữợ X ổ tæ ♣æ✱ A ❧➔ ♠ët t➟♣ ❝♦♥ ❦❤→❝ ré♥❣ ❝õ❛ X ✈➔ f : A×A → R ❧➔ ❤➔♠ ❣✐→ tr tỹ t ổ ữợ ❧➔ ✭❊P✮✱ ✤÷đ❝ ♣❤→t ❜✐➸✉ ♥❤÷ s❛✉✿ ✭❊P✮ ❚➻♠ x ¯ ∈ A s❛♦ ❝❤♦ ✈ỵ✐ ♠å✐ y ∈ A t f ( x, y) ỵ t ♥❣❤✐➺♠ ❝õ❛ ✭❊P✮ ❧➔ S ✱ tù❝ ❧➔✿ S = {x ∈ A : f (x, y) ≥ 0, ∀ y ∈ A}, ✹✳✶✳✷ ▼ët sè tr÷í♥❣ ❤đ♣ ✤➦❝ ❜✐➺t ❝õ❛ ❜➔✐ t♦→♥ ❝➙♥ ❜➡♥❣ ✹✳✶✳✷✳✶ ❇➔✐ t♦→♥ tè✐ ÷✉ ❈❤♦ X ✈➔ A ❣✐è♥❣ ♥❤÷ tr♦♥❣ ▼ư❝ ✹✳✶✳✶ ✈➔ ①➨t g : A × M → R✳ ❇➔✐ t♦→♥ tè✐ ÷✉ ✤÷đ❝ ♣❤→t ❜✐➸✉ ♥❤÷ s❛✉✿ ✭❖P✮ ❚➻♠ x ¯ ∈ K(λ) s❛♦ ❝❤♦ g(¯ x) = miny∈A g(y) ✣➦t f (x, y) := g(y) − g(x) t❤➻ ✭❖P✮ trð t❤➔♥❤ ♠ët tr÷í♥❣ ❤đ♣ ✤➦❝ ❜✐➺t ❝õ❛ ✭❊P✮✳ ✹✳✶✳✷✳✷ ❇➔✐ t♦→♥ ❜➜t ✤➥♥❣ t❤ù❝ ❜✐➳♥ ♣❤➙♥ ❈❤♦ X ✈➔ A ❣✐è♥❣ ♥❤÷ tr♦♥❣ ▼ư❝ ✹✳✶✳✶ ✈➔ g : A × M → X ∗ ✳ ❚❛ ①➨t ❜➔✐ t♦→♥ ❜➜t ✤➥♥❣ t❤ù❝ ❜✐➳♥ ♣❤➙♥ s❛✉ ✤➙②✿ ✭❱■✮ ❚➻♠ x ¯ ∈ A s❛♦ ❝❤♦ ✈ỵ✐ ♠å✐ y ∈ A t❤➻ g(¯ x), y − x¯ ≥ ❉➵ ❞➔♥❣ t❤➜② r➡♥❣ ✭❱■✮ s➩ trð t❤➔♥❤ ♠ët tr÷í♥❣ ❤đ♣ ✤➦❝ ❜✐➺t ❝õ❛ ✭❊P✮ ♥➳✉ t❛ ✤➦t f (x, y) := g(x), y − x ✳ ✷✽ ✹✳✶✳✸ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❝❤➼♥❤ ①→❝ ❚r♦♥❣ ♠ö❝ ♥➔②✱ ❝❤♦ X ❧➔ ♠ët ❦❤æ♥❣ ❣✐❛♥ ♠❡tr✐❝ t✉②➳♥ t➼♥❤✱ tù❝ ❧➔✱ X ❧➔ ♠ët ♠ët ❦❤ỉ♥❣ ❣✐❛♥ t✉②➳♥ t➼♥❤ ✤÷đ❝ tr❛♥❣ ❜à ♠❡tr✐❝ d ❝â t➼♥❤ ❜➜t ❜✐➳♥ q✉❛ ♣❤➨♣ tà♥❤ t✐➳♥ ✭tù❝ ❧➔✱ d(x + z, y + z) = d(x, y), ∀x, y, z ∈ X ✮ ✈➔ ✈ỵ✐ ♠é✐ ❞➣② ❤ë✐ tư (λm ) tr♦♥❣ R✱ (xm ) tr♦♥❣ X t❤➻ limm (λm xm ) = (limm λm )(limm xm )✱ Λ, M ❧➔ ❝→❝ ❦❤æ♥❣ ❣✐❛♥ ♠❡tr✐❝ ✈➔ A ⊆ X ❧➔ t➟♣ ❝♦♥ ❦❤→❝ ré♥❣✳ ❳➨t K : Λ ⇒ A ❧➔ →♥❤ ①↕ ✤❛ tr õ tr ỗ rộ f : A × A × M → R ❧➔ ❤➔♠ ❣✐→ tr tỹ ợ ộ (, à) ì M ✱ t❛ ①➨t ❜➔✐ t♦→♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè s❛✉ ✤➙②✿ ✭❊P✮ ❚➻♠ x ¯ ∈ K(λ) s❛♦ ❝❤♦ ✈ỵ✐ ♠å✐ y ∈ K(λ) t❤➻ f (¯ x, y, à) ợ ộ (, à) ì M t ỵ t ✭❊P✮ ❧➔✿ S(λ, µ) := {x ∈ K(λ) : f (x, y, µ) ≥ 0, ∀ y ∈ K(λ)}, ✣à♥❤ ỵ s t t ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t P ỵ t ❜➔✐ t♦→♥ ✭❊P✮✱ ❣✐↔ sû ❝→❝ ✤✐➲✉ ❦✐➺♥ s❛✉ ✤➙② ✤÷đ❝ t❤ä❛ ♠➣♥✿ ¯❀ ✭✐✮ K ❧➔ l.α✲❍☎ ♦❧❞❡r ❧✐➯♥ tử tr ởt N tỗ t↕✐ ♠ët ❧➙♥ ❝➟♥ U ❝õ❛ µ ¯ s❛♦ ❝❤♦ ợ x K(N ) U t f (x, Ã, à) h. ỗ m.1r tr conv(K(N )) ợ U t❤➻ f (·, ·, µ) ✤ì♥ ✤✐➺✉ tr➯♥ K(N ) × K(N )❀ ✭✐✈✮ f ❧➔ n.γ ✲❍☎ ♦❧❞❡r tr➯♥ U ✱ θ✲✤➲✉ tr➯♥ K(N ) ✈ỵ✐ θ < β ✳ ❑❤✐ ✤â✱ tr➯♥ N × U ✱ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❊P✮ ❧➔ ✤ì♥ trà ✈➔ t❤ä❛ ♠➣♥ ✤✐➲✉ r ợ (1 , à1 ), (2 , à2 ) N ì U t (S(1 , µ1 ), S(λ2 , µ2 )) ≤ ✹✳✷ 4ml h β α d β (λ1 , λ2 ) + n h β−θ γ d β−θ (µ1 , µ2 ) ❇⑨■ ❚❖⑩◆ ✣■➋❯ ❑❍■➎◆ ❈❹◆ ❇➀◆● P❍Ö ❚❍❯❐❈ ❚❍❆▼ ❙➮ ✹✳✷✳✶ ▼æ ❤➻♥❤ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè ❳➨t X, U, Z, M, Λ, E ♥❤÷ tr♦♥❣ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè✳ P❤÷ì♥❣ tr➻♥❤ tr↕♥❣ t❤→✐ ✭✸✳✶✮✱ ❣✐→ trà ❜❛♥ ✤➛✉ ✭✸✳✷✮ ✈➔ ✤✐➲✉ ❦❤✐➸♥ ✭✸✳✸✮ K(λ) = {z = (x, u) ∈ X × U s❛♦ ❝❤♦ ✭✸✳✶✮✱ ✭✸✳✷✮ ✈➔ ✭✸✳✸✮ ✤÷đ❝ t❤♦↔ ♠➣♥⑥✱ ✈➔ f : E × E × M → R ❧➔ ❤➔♠ ❣✐→ trà tỹ ợ (, à) ì M, t ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè s❛✉✿ ✭❊❈P✮ ❚➻♠ z¯ = (¯ x, u¯) ∈ K(λ) s❛♦ ❝❤♦ ✈ỵ✐ ♠å✐ w ∈ K(λ), f (¯ z , w, µ) ≥ ❚r♦♥❣ ♣❤➛♥ ♥➔②✱ ❝❤ó♥❣ t❛ ①➨t t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t P ợ (, à) ì M t ỵ t P S(, à) ✹✳✷✳✷ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè ỵ t t P sỷ r s ữủ t ỗ t↕✐ ❝→❝ ❤➡♥❣ sè ❞÷ì♥❣ T1 , T2 ✈➔ ❤➔♠ ❦❤æ♥❣ ➙♠ φ ∈ Lp ([0, 1], Rm ) s❛♦ ❝❤♦ |A(t)| ≤ T1 , |T (t)| ≤ T2 , |B(t)| ≤ φ(t) t ∈ [0, 1] ❤✳❦✳♥; ¯ ✱ tỗ t U ợ ❝➟♥ N ❝õ❛ λ ¯ s❛♦ ❝❤♦ ✈ỵ✐ ♠å✐ z ∈ K(N ) ✈➔ µ ∈ U¯ ✱ f (z, Ã, à) h. ỗ m.1 r tr ❝♦♥✈✭K(N )✮❀ ¯ ✱ f (·, ·, µ) ✤ì♥ ✤✐➺✉ tr K(N ) ì K(N ) ợ ộ ∈ U ✭✐✈✮ f ❧➔ n.γ ✲❍☎ ♦❧❞❡r tr➯♥ U¯ ✱ θ✲✤➲✉ tr➯♥ K(N ) ✈ỵ✐ θ < β ✳ ❑❤✐ ✤â✱ tr➯♥ N × U ✱ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❊❈P✮ ❧➔ ✤ì♥ trà ✈➔ t❤♦↔ ♠➣♥ ✤✐➲✉ ❦✐➺♥ r s ợ (1 , à1 ), (2 , µ2 ) ∈ N × U¯ , ρ(S(λ1 , µ1 ), S(λ2 , µ2 )) ≤ ( γ 4ml β1 β1 n ) d (λ1 , λ2 ) + ( ) β−θ d β−θ (µ1 , µ2 ) h h ❈❤ù♥❣ ♠✐♥❤✳ ❈❤ó♥❣ t❛ ❝❤✐❛ ❝❤ù♥❣ ♠✐♥❤ t❤➔♥❤ ✹ ữợ ữợ ợ t ự ữủ K() t ỗ õ rộ t r ữủ r ợ , trữợ ợ z1 = (x1 , u1 ) K(1 ) ổ tỗ t z2 = (x2 , u2 ) ∈ K(λ2 ) ✈➔ ♠ët ❤➡♥❣ sè l s❛♦ ❝❤♦ z1 − z2 ) ≤ l λ1 r ữợ ợ z11 ∈ S(λ1 , µ1 ) ✈➔ z21 ∈ S(λ2 , µ1 )✱ t❛ ❝❤ù♥❣ ♠✐♥❤ ✤÷đ❝ d1 := d(z11 , z21 ) ≤ 4ml h ✸✵ β d β (λ1 , λ2 ) ✭✹✳✷✮ ❙t❡♣✸✳ ❚❛ ❝❤ù♥❣ ♠✐♥❤ r ợ z21 S(2 , à1 ) z22 ∈ S(λ2 , µ2 ) t❤➻ n d2 := d(z21 , z22 ) ≤ h β−θ γ d β−θ (µ1 , µ2 ) ✭✹✳✸✮ ❙t❡♣ ✹✳ ❚❛ t❤➜② r ợ z11 S(1 , à1 ) z22 ∈ S(λ2 , µ2 )✱ t❛ ❝â d(z11 , z22 ) ≤ d1 + d2 ❉♦ ✤â✱ t❛ ❝â γ ρ(S(λ1 , µ1 ), S(λ2 , µ2 )) ≤ k1 d β (λ1 , λ2 ) + k2 d (à1 , à2 ), ợ k1 = 4ml h β ✈➔ k2 = n h β−θ ✳ ❍➺ q✉↔ ✹✳✶✳ ❳➨t ❜➔✐ t♦→♥ ✭❊❈P✮✱ ❣✐↔ sû r➡♥❣ ❝→❝ ✤✐➲✉ ❦✐➺♥ ✭✐✐✮✱ ✭✐✐✐✮✱ ✭✐✈✮ ❣✐è♥❣ ♥❤÷ tr ỵ tt ♥❤÷ s❛✉✿ (id ) A(t), B(t) ✈➔ T (t) ❧✐➯♥ tö❝ tr➯♥ [0, 1]✳ ❑❤✐ ✤â✱ t❛ ❝â ❦➳t ❧✉➟♥ tữỡ tỹ ữ tr ỵ ♥❣❤✐➺♠ ❝õ❛ ❜➔✐ t♦→♥ ✭❊❈P✮✳ ✹✳✷✳✸ ⑩♣ ❞ö♥❣ ✈➔♦ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ t❤❛♠ sè ❍➺ q✉↔ ✹✳✷✳ ❳➨t ❜➔✐ t♦→♥ ✭❖❈P✶✮✱ ❣✐↔ sû ❝→❝ ✤✐➲✉ ❦✐➺♥ s❛✉ ữủ t ỗ t số ❞÷ì♥❣ T1 , T2 ✈➔ ❤➔♠ ❦❤ỉ♥❣ ➙♠ φ ∈ Lp ([0, 1], Rm ) s❛♦ ❝❤♦ |A(t)| ≤ T1 , |T (t)| ≤ T2 , |B(t)| ≤ φ(t) t [0, 1] ; tỗ t U ợ N s ợ U g(Ã, à) h1 ỗ m1 r tr➯♥ ❝♦♥✈(K(N ))❀ ✭❝✮ ✈ỵ✐ ♠å✐ z ∈ K(N )✱ g(z, ·) ❧➔ n1 γ1 ✲❍☎ ♦❧❞❡r tr➯♥ U¯ ✳ ❑❤✐ ✤â✱ tr➯♥ N × U¯ ✱ →♥❤ ①↕ ♥❣❤✐➺♠ ❝õ❛ ✭❖❈P✶✮ ❧➔ ✤ì♥ trà ✈➔ t❤♦↔ ♠➣♥ ✤✐➲✉ ❦✐➺♥ r s ợ (1 , à1 ), (2 , µ2 ) ∈ N × U¯ , ρ(S(λ1 , µ1 ), S(λ2 , µ2 )) ≤ ( γ1 4m1 l1 β1 β1 n1 ) d (λ1 , λ2 ) + ( ) β1 −θ1 d β1 −θ1 (µ1 , µ2 ) h1 h1 ✸✶ ❑➌❚ ▲❯❾◆ ◆❣♦➔✐ ♣❤➛♥ ♠ð ✤➛✉ ✈➔ ♣❤➛♥ tê♥❣ q✉❛♥ tr➻♥❤ ❜➔② ð ❝❤÷ì♥❣ ✶✱ ✤➲ t➔✐ ✤➣ t❤✉ ✤÷đ❝ ♠ët sè ❦➳t q✉↔ s❛✉✿ ✲ ❚❤✐➳t ❧➟♣ ✈➔ ❝❤ù♥❣ ♠✐♥❤ ✤÷đ❝ ❝→❝ ✤✐➲✉ ❦✐➺♥ ✤õ ❝❤♦ t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè✳ ❙❛✉ ✤â →♣ ❞ư♥❣ ❦➳t q✉↔ ✤↕t ✤÷đ❝ ✈➔♦ tr÷í♥❣ ❤đ♣ ❝ư t❤➸ ❜➔✐ t♦→♥ ♥❤÷ tr♦♥❣ ❜➔✐ ❜→♦ ❝õ❛ ♥❤â♠ t→❝ ❣✐↔ ❇ò✐ ❚rå♥❣ ❑✐➯♥ ✈➔ ❝ë♥❣ sỹ t ữủ t q t ữủ ợ ✈➔ ♠↕♥❤ ❤ì♥✳ ✲ ▼ð rë♥❣ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè t❤ỉ♥❣ q✉❛ ✈✐➺❝ t❤✐➳t ❧➟♣ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ ❝➙♥ ❜➡♥❣ ♣❤ö t❤✉ë❝ t❤❛♠ sè ✈➔ ✤÷❛ r❛ ❝→❝ ✤✐➲✉ ❦✐➺♥ ✤õ ❝❤♦ t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t♦→♥ ✤✐➲✉ ữợ rở ự t ◆❣❤✐➯♥ ❝ù✉ ✤✐➲✉ ❦✐➺♥ ✤õ ❝❤♦ t➼♥❤ ❧✐➯♥ tö❝ ❍☎♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ①➜♣ ①➾ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè✳ ✣➙② ❧➔ ✈➜♥ ✤➲ rt õ ỵ tỹ t tổ tữớ t r➜t ❦❤â t➻♠ ✤÷đ❝ ♥❣❤✐➺♠ ❝❤➼♥❤ ①→❝ ❝õ❛ ❝→❝ ♠ỉ ❤➻♥❤ t♦→♥ t❤ü❝ t➳ ❦❤✐ ❝→❝ ❞ú ❦✐➺♥ t❤✉ ✤÷đ❝ ❝â s❛✐ sè✳ ◆❣♦➔✐ r❛ ❝â t❤➸ ♥❣❤✐➯♥ ❝ù✉ t➼♥❤ ✤➦t ❝❤➾♥❤ ❝õ❛ ❜➔✐ t♦→♥ t❤❡♦ ♥❣❤➽❛ ❜➔✐ t♦→♥ ❝â t ỗ tớ ✤➲✉ ❤ë✐ tö ✤➳♥ ♥❣❤✐➺♠ ❞✉② ♥❤➜t ♥➔②✳ ✸✷ ❈➷◆● ❚❘➐◆❍ ❈➷◆● ❇➮ ▲■➊◆ ◗❯❆◆ ✣➌◆ ✣➋ ❚⑨■ ◆●❍■➊◆ ❈Ù❯ ✶✳ ❇→♦ ❝→♦ t↕✐ ❍ë✐ t❤↔♦ ❚♦→♥ ❤å❝ q✉è❝ t➳✿ ❖♥ ❍♦❧❞❡r ❈♦♥t✐♥✉✐t② ♦❢ ❙♦❧✉t✐♦♥ ▼❛♣ ♦❢ t❤❡ P❛r❛♠❡tr✐❝ ❊q✉✐❧✐❜r✐✉♠ ❈♦♥tr♦❧ Pr♦❜❧❡♠✳ ■♥t❡r♥❛t✐♦♥❛❧ ❲♦r❦s❤♦♣ ❱❛r✐❛t✐♦♥❛❧ ❆♥❛❧②s✐s ❛♥❞ ❖♣t✐♠✐③❛t✐♦♥ ❚❤❡♦r②✱ ❱✐➺♥ ❚♦→♥ ❤å❝✱ ❍➔ ◆ë✐✱ ✶✷✴✷✵✶✼✳ ✷✳ ❇→♦ ❝→♦ t↕✐ ❍ë✐ t❤↔♦ t♦→♥ ❤å❝ ❝❤✉②➯♥ ♥❣➔♥❤✿ ❖♥ ❍♦❧❞❡r ❈♦♥t✐♥✉✐t② ♦❢ ❙♦❧✉t✐♦♥ ▼❛♣ t♦ ❛ P❛r❛♠❡tr✐❝ ❖♣t✐♠❛❧ ❈♦♥tr♦❧ Pr♦❜✲ ❧❡♠✳ ❚è✐ ÷✉ ✈➔ t➼♥❤ t♦→♥ ❦❤♦❛ ❤å❝ ❧➛♥ t❤ù ✶✻✱ ❇❛ ❱➻✱ ❍➔ ◆ë✐✱ ✵✹✴✷✵✶✽✳ ✸✳ ❇➔✐ ❜→♦ ❣û✐ ✤➠♥❣ tr➯♥ t↕♣ ❝❤➼ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❈➛♥ ❚❤ì✿ ▲➙♠ ◗✉è❝ ❆♥❤✱ ◆❣✉②➵♥ P❤ó❝ ✣ù❝✱ ❱ã ❚❤➔♥❤ ❚➔✐✱ ❚r➛♥ ◆❣å❝ ❚➙♠✳ ❚➼♥❤ ❧✐➯♥ tö❝ ❍☎ ♦❧❞❡r ❝õ❛ →♥❤ ①↕ ♥❣❤✐➺♠ ❜➔✐ t♦→♥ ✤✐➲✉ ❦❤✐➸♥ tè✐ ÷✉ ♣❤ư t❤✉ë❝ t❤❛♠ sè✳ ❚↕♣ ❝❤➼ ❦❤♦❛ ❤å❝ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❈➛♥ ❚❤ì✳ ✸✸ ❚⑨■ ▲■➏❯ ❚❍❆▼ ❑❍❷❖ ❆❞❛♠✱ ❘✳ ❆✳ ✭✶✾✼✺✮✳ ❙♦❜♦❧❡✈ ❙♣❛❝❡s✳ ◆❡✇ ❨♦r❦✿ ❆❝❛❞❡♠✐❝ Pr❡ss✳ ❆❧❡❦s❡❡✈✱ ❱✳ ▼✳✱ ❚✐❦❤♦♠✐r♦✈✱ ❱✳ ▼✳ ❛♥❞ ❋♦♠✐♥✱ ❙✳ ❱✳ ✭✶✾✽✼✮✳ ❖♣t✐♠❛❧ ❈♦♥tr♦❧✳ ◆❡✇ ❨♦r❦✿ ❈♦♥s✉❧t❛♥ts ❇✉r❡❛✉✳ ❆✉❜✐♥✱ ❏✳P✳✱ rs t ss st raăsr P✳◗✳✱ ❱❛♥✱ ❉✳❚✳▼✳✱ ❨❛♦✱ ❏✳❈✳ ✭✷✵✵✾✮✳ ❲❡❧❧✲♣♦s❡❞♥❡ss ❢♦r ✈❡❝t♦r q✉❛s✐❡q✉✐❧✐❜r✐❛✳ ❚❛✐✇❛♥❡s❡ ❏♦✉r♥❛❧ ♦❢ ▼❛t❤❡♠❛t✐❝s ✶✸✱ ✼✶✸✲✼✸✼✳ ❆♥❤✱ ▲✳◗✳✱ ❆✳❨✳ ❑r✉❣❡r✱ ❆✳❨✳✱ ❚❤❛♦✱ ◆✳❍✳ ✭✷✵✶✹✮✳ ❖♥ ❍☎ ♦❧❞❡r ❝❛❧♠♥❡ss ♦❢ s♦❧✉t✐♦♥ ♠❛♣♣✐♥❣s ✐♥ ♣❛r❛♠❡tr✐❝ ❡q✉✐❧✐❜r✐✉♠ ♣r♦❜❧❡♠s✳ ❚❖P✱ ✷✷✱ ✸✸✶✲✸✹✷✳ ❆♥❤✱ ▲✳◗✳✱ ❑❤❛♥❤✱ P✳◗✳✱ ❚❛♠✱ ❚✳◆✳ ✭✷✵✶✺✮✳ ❖♥ ❍☎ ♦❧❞❡r ❝♦♥t✐♥✉✐t② ♦❢ s♦❧✉t✐♦♥ ♠❛♣s ♦❢ ♣❛r❛♠❡tr✐❝ ♣r✐♠❛❧ ❛♥❞ ❞✉❛❧ ❑② ❋❛♥ ✐♥❡q✉❛❧✐t✐❡s✳ ❚❖P✱ ✷✸✱ ✶✺✶✲✶✻✼✳ ❇❧✉♠✱ ❊✳✱ ❖❡tt❧✐✱ ❲✳ ✭✶✾✾✹✮✳ ❋r♦♠ ♦♣t✐♠✐③❛t✐♦♥ ❛♥❞ ✈❛r✐❛t✐♦♥❛❧ ✐♥❡q✉❛❧✐t✐❡s t♦ ❡q✉✐❧✐❜r✐✉♠ ♣r♦❜❧❡♠s✳ ▼❛t❤❡♠❛t✐❝s ❙t✉❞❡♥t✱ ✻✸✱ ✶✷✸✲✶✹✺✳ ❈❡s❛r✐✱ ▲✳ ✭✶✾✽✸✮✳ ❖♣t✐♠✐③❛t✐♦♥ ❚❤❡♦r② ❛♥❞ ❆♣♣❧✐❝❛t✐♦♥s✳ ◆❡✇ ❨♦r❦✿ ❙♣r✐♥❣❡r✳ ❋❛♥✱ ❑✳ ✭✶✾✼✷✮✳ ❆ ♠✐♥✐♠❛① ✐♥❡q✉❛❧✐t② ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥s✳ ■♥✿ ❙❤✐s❤❛✱ ❖✳ ✭❡❞✳✮ ■♥❡q✉❛❧✐t② ■■■✳ ◆❡✇ ❨♦r❦✿ ❆❝❛❞❡♠✐❝ Pr❡ss✳ ❑✐❡♥✱ ❇✳ ❚✳✱ ❚♦❛♥✱ ◆✳ ❚✳✱ ❲♦♥❣✱ ▼✳ ▼✳ ❛♥❞ ❨❛♦✱❏✳ ❈✳ ✭✷✵✶✷✮✳ ▲♦✇❡r s❡♠✐❝♦♥t✐♥✉✐t② ♦❢ t❤❡ s♦❧✉t✐♦♥ s❡t t♦ ❛ ♣❛r❛♠❡tr✐❝ ♦♣t✐♠❛❧ ❝♦♥tr♦❧ ♣r♦❜❧❡♠✳ ❙■❆▼ ❏✳ ❈♦♥tr♦❧ ❖♣t✐♠✱ ✷✽✽✾✲✷✾✵✻✳ ◆✐❦❛✐❞♦✱ ❍✳✱ ■s♦❞❛ ❑✳ ✭✶✾✺✺✮✳ ◆♦t❡ ♦♥ ♥♦♥✲❝♦♣♣❡r❛t✐✈❡ ❝♦♥✈❡① ❣❛♠❡s✳ P❛❝✐❢✐❝ ❏♦✉r♥❛❧ ♦❢ ▼❛t❤❡♠❛t✐❝s✱ ✺✱ ✽✵✼✲✽✶✺✳ ◆❣✉②➵♥ ✣æ♥❣ ❨➯♥ ✭✷✵✵✼✮✳ ●✐→♦ tr➻♥❤ ❣✐↔✐ t➼❝❤ ✤❛ trà✳ ❍➔ ◆ë✐✿ ◆❤➔ ①✉➜t ❜↔♥ ❑❤♦❛ ❤å❝ ❚ü ♥❤✐➯♥ ✈➔ ❈ỉ♥❣ ♥❣❤➺✳ ❱ơ ◆❣å❝ P❤→t✳ ✭✷✵✵✶✮✳ ổ ỵ tt t ✣↕✐ ❤å❝ q✉è❝ ❣✐❛ ❍➔ ◆ë✐✳ ✸✹