Lectures on Nonlinear AnalysisSample

Pavel Drábek Jaroslav Milota.[r]

Lectures on Nonlinear Analysis Pavel Drábek Jaroslav Milota
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k5   S5 C E   Q Q'@ ;  E N G= C N ;N; = N Q Q'E  C 87 E C E C D;  C69 &A  ; = 7'9 = ;  09 E @ C = @ C6C 87:9 ; @ N 87:9 ; @ N & F  ; CH7 ; = G=  E C = 7:9?C N ; @ <B< *   A " "   +* & '& '& <   `   &         $ +   +  $  "   &  7 *+*  E @ < ; HC =6; E  = 7:9 = E ;  & & REZE   ( #"I%$+*!,   $  & !  k5 ' % & +, &  $ T "  *+* ( & " $ '&  f*  &  S5   f* S5  N S57 :-:; k@ N   +*  9 0= 7:9 ; <B< ; E  R=  C E ;  ;  +* " @ ; Q ; C E- G+ "  1R+ b *U/ :,  +   J5 ! * F *F + # *:, /F 8- *!,:* 57    S57  f* N   +*  * i  =3S3 D + S * ,X/,   *)F ? K ,2 ; %   i     * i   )(+*-,/.1023,124.65C[87+v902+: c ; : r<; r +: = `?> J2 oqp n c'p LK M ƒ :?N Ä›Ä›Ä N D m]  c2 s `7c `     c 2,) c [A@B.'[8:C7,/: ƒ N ÄZÄ›Ä N s <%  Z  F * /   *+* ( -, % i F  7 : % @ w g * + * oqp r  i  i * + *  =  6 *+* ( #6 7:J; [ `7o w DGF n`7c [ `?Hmo 2+,!.1: ,!: E I ` ^ ` ;7F7   mc : o <[ ; & `   .J2 "  %/!+,* AM$&% >F +   5  & = 7:9?C (S N E F9   *   \* ; @ ; ; C E= E;  & C B< < + A = / * + *+*  -,  *   
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' <BE  @  $   *   7:9 @   Q+ -,    ,      < :@ E N A:< = E Q:<ZE E = ; = 7:9?9 E  <ZA  ;  ; = E = G=[= 7:9 87 E C ; <B< ; C E NPN E = < @ ; N   E = E ;  &   @ E C69  - N Q Q:E  / 57 57 E 7 C  f C N @ 9DC A:< = E C = @HA 7:9  E C @ Q:<   ;E C < G= 9 @ ; G= i J  >  =  57  \ E C @ Q:< C A E < C N B< < B< < \ i  W C A = G=  = 7:99 &A G= E ;  i <B<k  N < i  EC C A  E RA C ; <BA = E ;  E = E C < ; C69 i E  = E   @ = 7:9CH97 )Q ;G= 7:9DC69C 9 !   P9 &V  & " $
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 & *)  '  \ i  W   *    Q+ :, 7'9 @  #"%$ & (' )$*",+ - )/ + - /" $ <Z< 8& " !  *&   + 3< ' 36 * 7 + B, $   39  D  $ !   !Z$   i ,         !    ; = 7:9?9 &A10 = E ; 3254 i76 "   #6 < , &  98  ;: =  =< 0>< ; A @? ? ; Q  C A@< C69 = ; 57A0 @? < =  < <BE  @ C A@< C Q@0 ; 57 = =  54  E C C A = =  4 :; = 9CB Q'@ ; D= E ;  ; 57 ; >=6;   = :7 @ 9DC = @6E = E ;  ;  ; >=6; 4  B 6i 8G 7:9   @?EDF4 i76 B i76  ? 4HD  I?  & 8KJ   G ; C699 = E C :; = ,E L ,@ C = = = $ " $      (   AQ Q ; C69 > & f* & "  , *+* N   , > N * & " * N  > ,   > ) , ) @?m4O & 8KJ + K ) U; @    g D D 4  4  M? = = < ;G= C E ? 9DC E N4O & 8PJ @ ?   ? 8RQTS = g7'9 L ; C = @6A@g L = E ; ); UV? 9XW @ 99 RE = C AMYZL 9C ] A10 <BE = S A @? @ = 7:9 ?@? E = E ; <^0 C6C A NPQ = E ;  C /   @?  E C @ 9XW A'<_0 @ [ 0G<BA D 4` ba c `edfc a d a  `    a ih @ B Mj 9e"W = ? =1D k? = c l U ; <Z< ; j C   ,@ N G EC N  C =6; Q:@ ;\[ = 7:9 E L & " ? ) > ) , *  n :A @  R= E N E C = ; "W  @0 <ZE = 7:9 '; = E ; ?;)U@? W @ 9D9 6= ;  E    E = ? E N  C E ;  0G< C Q10L E  L = 7:9 Q @ ; Aoj @ G 7:9 ; @ N E C 0pL ; @ ; <Z<_0 @ S ;)U = 7:9 ; N ; =6; Q S E o[ @6E,0  L Q'@ ; Q @ = S ;)U = 7:9 ? 9XW @ 99 @? Hq+*-@B ;.r ; , :?7 1: tstv u r <xwy @ l 902 2 , , > 1: @02+@ > 10 A, z I j`7oqoqp s s Rv c `#^ ` c [ ` e g ^ ehg ` m[ ^ r j`#o [ p#r J ! -

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v u q @  † u   @ ~ †  <  @ ! † y 7– s ) ? x , x ˆ’ M ’n M  +}| 62J 7 0< F#+ 3 y@CB 7– s )? x , x ! & M M  U ) V+  UW )_Xe U +  F ^ 3'H + xI'6kx S† !%   x ) * ) )       z yxgz%"/  ‘ M  $  " Ž & ),Ž M ’! c" Žg$ 4'& (‘ "($ xvJ <7XYX) 3U™6 u x Z @gx v b u  UW6 & †’  M x¤n Ž ‘ & M ’'$yx z ’ M ’{" & Ž m k ln & M ’'$ x , + U Xe  3; )  ) 7 (5 D W D  } xT < 3'^ Xe ]c5 + ) 3U + i 5-u Œ ) (5 W*3 +  F x 7 F <C8 x@C7B B ] )_ + )  Z ha.0<C8 , s F#+ W + 3*^mxŽ@CB [ B'6 1 ) )  @ [~ † Hcx  6vu ]c5(W ¨ <> 8a7 U j x I'6 Œ xM ’{" & Ž f " Ž & Ž$ x | < F ,~ Ut1x  )_ + )  " ’{" Ž & pS "Ž  x  + # F  +  143U ) ) 3'5 ), s W + 3*^mx )_8;:=<7.0? b—T < 3*H < 3cb'] q H*3 ) q b Œ <7.0< 3U < xv@™B u [  @CB  † Hcx  6'u ]c5(W ¨ <> 8a7 U j xI'6 Œ xM ’{" & Ž f " Ž & Ž$ x | < F ,7 Ua101xc143ƒU )  + ) 3*5 )-, s F#+ W + 3*^mx  )98„:=<>./? bcT < 3*H < 3cb—] q H*3 ) q b Œ <>./< 3U < x¢@CB v ED q  |  x0TN6JK6kx & M & h M j  Q Ž " Ž" ’ M & kmln & M ’'$ x  XY)_ +   UW )XY U +  F ] < + ) U q x ,.0< |c+ ˜  F [ H ) 3'5 ) x VW < H )  3*HcxA@CB7B ED @  + U e U + x 6 x y j  ? ,       M ’{" & Ž M  & M ’  & ’† M x¤nŽ ‘ & M ’ z x  < F+ )7   F 6!" Ÿ@CB [>[ xŽ@ @9b2@ [ } ED>D  F#F 3*Hcx x w <  o ˆ!nŽ$C" M ’ w $ Ž & ‘ # & Ž ’ M ‘ w ’ &  $ M $ xYJm J ,./) 0 x ha<    U < 3cx F <7 + H  xŽ@™B>B u ED v  5>$ – x]Ž6 x2 & M M  › ? ! yxmz ’ M ’{" & Ž  k ln & M ’'$ & ’† !n’† & Ž &% & §n"VQŽ #"/g$ xƒ†t6ƒ ) + H ) F , s F#+ W + 3*^J <>X e  q x2† <7 H /) 5(WTU x < F#F  3*cH xŽ@CB [ q ED }  5>$ – x]Ž6 u ' x  6kx ¨ ) z ’ M ’{" & Ž h M j " Ž" ’ M & kmln & M ’'$ x F# ) |c+ )_ x  X  U ) H 7X b f › ? Hcb  ¨ <7 )_8 :=<>.0? xA@CB [ q ED  5>$ – x]Ž6‚u   x(I'6 x y  & & ’† ’
’ M ’{" & Ž " M c" ’ & §n" M  M u › ? z x )>U› W{  5(W *6 )2nƒœ $ 4Ÿ" @CŽ1B ’ D( x D ‘ ’ b ŽD "9[ B' ’ˆ’ "Ž"/ Ž  #"/g$   ED ~ 5>$ – x]Ž6 x   x(I'6 xc] x(I'6 xƒu ] x ` 6kx* › ?  )>›  < › )? < › )? " ‘` Ž & w ’ &  $ M \ $ yx= z ’ M ’{" & Ž f " Ž & ,Ž($ x T ) 5_U 0) < U )  +  UW )XY U + VZ v } x2] e + 3*^ ) )_ F  m^ x h‡) F+ 3cb )_8d:=<>./? xA@™B v ED ! o% + )  x- 6‡u ™8 W + 3
x(I'6 x ˆ M ’
‘ M c" h "  Ž"(" & ’†`  z ’ M ’{" & Ž h  M j " Ž" ’ M & akmln & M ’'$ x  + T ) 5_U 0) < U )  UW )XY U + VZ u >[ x2] e + 3*^ ) )_ F  m^ x h‡) F+ 3cb )_8d:=<>./? xA@™B ED [~ +F ^mx0†t6 u Œ H + 3*^ x  6]Ž6kx M M & M & h M j o s~ ` ) k‡‹ ‘aQ Ž " Ž(" ’ M & k ln & M ’'$yx  "‘’† f Ž{c" Ž x e] + 3*^ )_ ) F  m^ x ha) F#+ 3cb  ) + H ) F s ) ^!b  )98 :=<>.0? x D qgq @>6 ED B  o- + e ) s ) ^x(JK6 x{T <  3*H ) Hcx]Ž6 xu ]cU    x x % ! 4" Ž1Ž & ’ y"  Ž & & ’† L n ’
‘ M ’ & {k ln & + M ’'$ xJ 7Xts* + H*^ ) +| ) 0+ U q ,N./) / xŽJ 7Xts* + H*^ ) x@CB7B q  vgq    ` 7s* F  x , x  – )_? x , x*uŠ + j F ) x x  ’ Ž Y7n ‘ M ’  & ’ & ‘  '& ‘("($ x | < F 6ƒ1(6  3'He101(6 x  UŸ˜ ¨ q j e /) 0 x ,N.0 W  xA@™B>B ) ) ) J ) ) () ;3 ) ) J ) J ) J * ) ) K1 J ) $ ) J ) )N3 * J 4 ) ) ) $ ) ) ) ) $ 5 ) ) ) ) ) ) &) ) 
     v u @   v @   F  x x LNM M + h M `      X < , ’ 4" e" ’'$ M ’ & % " ‘ ,Ž  '& ‘("($ x  < U  3'Hcx , + 3*5 ) U < 3cx )_8 I )  ) q x @CB q v D   y z 7X +F U < 3cx-6(] 6kx D S " M ’ D>7D7" DŽ$C" x¤n ’
‘ M ’ "Ž("/ yx z C$ & ’† ŒKC$C" Ž x h *FF  X) 6  UW6 ] < 576
Ÿ@CB [ x u b  vgv   +  5(Wcx 6 x h M j `  " Ž" ’ M & ‡S† !%   2x ] e + 3*^ ) )_ F  ^mx h‡) F+ 3cb )_8d:=<>./? xA@™B  v }  – x(I'6  x M & M j) x¤n Ž ‘ ’ S "Ž  xTŽ L Ž"  ˆ!  f " Ž & Ž$ x )_X  XY)_  UW6c] < 576 Z @ } x  XY)_ +   U0W )XY U +  F ] < + ) U q x ,.0< |c+ H ) 3*5 ) x  W < H ) /F  3'HcxA@CB @76 v  ' U x Œ 6x `  u  < QV" Ž n Ž & M ’ S "Ž  xTŽ M ’{" & Ž f " Ž & Ž$ xg] e + 3*^ )_ ) F  ^x ha)_ F+ 3cb )_8 :=<>./? xA@CB  v ~ ' FF q x(I'60T6kx  `   ) ) " ’{" Ž & aS† !%   x  <  U  3'Hcx , + 3'5 ) U < 3cx )_8 I )_  ) q x¢@CB u ) ) ;3 > * ) ) ;3 ) ) ) )C3 (3 ) ) ;3 )  v ! '   F + x  6kx   < ) ? S† !%  M ‘ & NŒ " ˆY!$ M ’ " S "Ž  yxez ’ M ’{" & Ž  ’ 4"  f M ’'$ x ,)_ ^ ~XY< 3
x ¨ <> HcxA@CB }  v [~ '   F + x  u   < ) ` ? ~s*.0) + ?7< x , , x  " e" Ž M ‘;Œ " ˆY!$ yx„z ’ M ’{" & Ž  ] e + 3'^ ) )_ F  ^mx ha)_ F#+ 3cb )_8d:=<>.0? xA@CB [ } v B  ' x(I'6 x S "Ž  yx h "  Ž"("($ M w M ‘ & M ’'$  M x¤nŽ ‘ & ™8 )98 + j x 6‡u  h M j " Ž" ’ M & Žkmln & M ’'$ x2I < W'3 +F#F ) q u¡] <  x )98;:=<>.0? xA@CB7B  }‚q  ' x  x{I W*3cx x2u 57› $ – ? x(]Ž6 x{L n’
‘ M ’  '& ‘("($ x   H )_X +  x ,.0 ^ ) xA@CB u ¨ )_ < )C3 $ )N3 ;3 Ž & ‡kmln & + ) ) ) > > ) w ’ &  $ M$ x ;3 )N3 )N3 ) !) > ) ) $ J ) M ’'$ & ’†  } @  T *3 H  3cx  6u£T y  ) XY  j)_ x  z 6(JK6 x z ’ M ’{" & Ž "  Ž n & M ’'$=yx M ’{D " & Ž¥"9‹ M M ‘ !n ’† & Ž  & §n" Ž  #"/g$ & *Ž("($!’ & ’
‘(" x2I'6  UW6 ) 5(W6  y@CB q x q BCb v } D  T ?~)~ › xI'k6 x & ‰ M $   x¤n’ ‚‘ M ’ & ‰ ’  ‰ & ’ &  ‰   x ' 7.0< F#+ X x ,N.0 W  xA@™B>B [  + 3šJ j) 5(W  }‚v  T * U + x0TN6 u ] ` ) ? <>sŽ< F ) | x x ka#"/e" ’ ‹$2yx L n’
‘ M ’  & w ’ &  $ M $ x <  <C8 xv@CB u  +  * ˜ /+  3  3'^ F#+ W©U 0 0F  U + < s q I < W*3 +#F ) q u ] <  x )98;:=<>./? @CB }  }g}  ™8 W + 3cx(I'6 x S† !%  M ‘ & h "  Ž"("-Œž" ˆY!$ M ’iz ’ M ’{" & Ž !n’† & Ž  % & §n"-Q Ž  #"/g$ xŽ ) ˜ ^ + <  F J < ¨ ).0) 3*5 ) ] ) + ) +  UW )_Xe U +  Z }‚q x  X) +   UW )_Xe U +  F ] < + ) U q x ,.0< | ˜ + H ) 3*5 ) x2VW < H ) 0F  3*cH x@CB B'6 }  ` `   u  j ”  x o 6kxV  !#" $ '& ‘("($ x=] e + 3*^ ) ) F  ^mx ha)_ F+ 3cb ) + H ) F sŽ)_ ^!b )_8 :=<>./? b Œ <7? q < x @CB [ u  } ~ +F x(I'6 x  ` <7 S† !%   x1Ž   " h M j " Ž" ’ M & #" % M "   M ’ x +| ) 0+ U q <7¨ + ^ + +  ,N./) / x JaW ~ F < U0U ) /|c+#FF ) x{@CB u  } ! y <  ) x(I'6 x w zŽ & M '  ‘’ 7" Ž c" ’ M 4" Ž & M ’ e" ˆY & ’†6’
 ’ M ’{" & Ž D '& Ž M &  M j " Ž(" ’ M & "0ln & M ’'$   0 x  3*36 ]—5 < F  <>.0X 62] e , +  J F 6]—5 + *6 " Ÿ@CB x u b v @ u x } B>B b u v u 4 * ) ) ) ) ) ) > )C3 * 4 )C3 ) * ) ) ) ) )N3 ) ) ) 
v u D  } [~       >) ›   x(I'6 x
 "($  " ‰ ˆYc"($  M Ž"‘ 4"($ " ’ "!‰ Ž M " c"($ "‰ ln & M ’'$ "9‹ M M ln2"($ x  0 < ) URJ ‘“’ x ,7 +# x@CB  } B   + ^mxT6 x  0) s ) †S  M ‘($ M ’©z ’ M ’{" & Ž L n ’
‘ M ’ & w ’ &  $ M $ x—J <  3ƒUa143  U + U U ) x )_8 :=<>./? x @CB }  q   u ,.0< U/U ) x  6%u ) + s ) ^ ) x 6 x Œ & O>M Rn  QŽ M ’
‘ M #" M ’ h M j " Ž" ’ M & -kmln & M ’'$ x ,.0) 3U + )  F#F x 3*^ F )_8‡<—< HšJ F#+ x{@™B  @   +3 +U x  6x u ~s  <C8 j , ˆ’ Ž M n M ’ M ’ z'’ M ’{" & Ž L n ’
‘ M ’ & w ’ &  $ M $ x   H )_X + ,./) 0 x 143*576 x )98„:=<>./? xA@CB @>6  D   Hcx 6¢u ] + 3cx 6kx & "/ & M ‘ & vQ  $ M ‘($ x | < F 6{1 ` x   H )_X + u )_)  X < h ž Œ " ˆ Y  !  $ y  % x K Œ Y  c  " Ž ž ’ Œ  ,.0) / x2143*5~k6 x )_8;:=<>./? x@CB 7[  v    u < ?7)9¨ ) FF 7 x-6 Œ x ˆ’ 7" Ow ’ &  $ M $ x , + 3*5 ) U < 3 +| ) 0+ U q ,.0) 0 x , + 3*5 ) U < 3cx )_8 I ) ˜  ) q xA@CB q  }   H + c3 x k6 x L   u n ’
‘ M ’ & w ’ &  $ M $ x op.™8 b +F#F x )_8;:=<>./? xA@CB v    H + 3cx 6kx
& &   ugu " ’†šˆ  #" ORw ’ &  $ M $ x op.™8 b +#F#F x )_8;:=<7.0? x@CB }  )N3 ) )C3 ) ) ) J > ) ) ) ) ) )C3 )N3 ) * > ) >  ~   UYx Œ 6Žu ] + F x 6kx¢ u ?~)  !#"  '& ‘("($yx L Ž & ‘ M ’ & f Ž{c" Ž  z%"/  ‹$  M Yf " Ž & Ž$ & ’† h & & & M j " Ž" ’ M & 2kmln & M ’'$ x  F U )_ H )%op —q U ) x ha) F#+ 3cb )98 :=<>.0? x@™B>B z'’ M ’{" ŽVQ Ž M  ! ] cH x  6kx y z u 7 S " e" & $9D nŽ" yx "M‘ Ž M M ‘ & c$C" & §n2"($yx\ M j " Ž" ’ M & : & M ’!$ x h *FF  X)  U0W62] < 576 y@CB } x [>[ v b [ B q  [~ ] W'^ F x y  w vO "   M ’ "Ž"/ xTŽ & M ’  M & ‘’ Ž & ‘ M 7" M 4" Ž & y" z x ,.0< 576  X) u )   U0W62] < 57*6 "2œ y@CB B x v @9b v }  B  ] + 3'^ x01(6 x u ) ‚"($ w ` Ž O>M  & M ’ M  ’ z'Že"  M ’{" & Ž  '& ‘("($  k‡#"/e" ’ ‹$ yx M ’{" & Ž  n + $ '& ‘("($ x] e + 3'^ ) )_ F  m^ x ha)_ F#+ 3cb )_8d:=<>.0? xA@CB q  q  ]cU – xI'6gu I W*3
x 6kx L ~  < n ’ ‚‘ M ’ & ‰ ’  ‰ & ’ &  ‰  & z"9 M ’{" & ‰ Ž1’  ‰ nc‰ %  x¥]cU2 – U03A$ – e ) H  ^ < ^ + ? ) – 7? F  H  U ) F# U | $ – x ,N.0 W  x{@CB [  + 3šJ j) 5(W  @  ]cU + c3 x 6 x'2M ) ’7nc & Ž  ’ y"  Ž &  $ & ’† h M j " Ž(" ’ M & M M  QŽ  " Ž M "($\yx L n’
‘ M ’'$ x ,N + 3*5 ) U <  +}| 0+ q  )_ U ,.0)  x , + 3*5 ) U <
3 x )_8 I )  ) q x@™B q  D  ]cU ^ x(]Ž6 x   )_ s ) "‘ n Ž"($’ h M j " Ž(" ’ M &  " e" Ž  x ,.0) 3U + )  F#F x 3'^ F )98a<c< HRJ F#+ x'@™B u  v  Œ + F x  6kx D  )_sŽ) S "Ž  yx L n’
‘ M ’  '& ‘("($ x | < F  3*Ht1/1x h + 0? W  ' ) x hm  ) F x*@CB [ v  3*H¥@™B>B  }  ` | H x U F 6kx ) <  )  QV " Ž M Y M ‘  !§n M ’'M $ yx‡Q & Ž M & h  M j " Ž" ’ M & ck ln & M ’'$ RS M e" QV" Ž M Y M ‘  e + K  F  !§n M ’'$ x2] UW < W ) 7 3šH ) 3š q c3 xA@CB [ @>6 <c<>.0 W < x   `  u :=< 0+ H  x ' xŽL n’
‘ M ’ & w ’ &  $ M $ x2] e + 3'^ ) )_ F  m^ x ha)_ F#+ 3cb )_8d:=<>.0? xA@CB u > ) ;3 )  ) ) ) ) )C3 ) ) ) > ) )N3 4 * * ) )N3 ) ) * ) ) ) ) $ ) ) ) ;3 ) ) ) ) ) ) $ ) ) 5 ) ) ) ) 
     v u v   ~  + H F x k6 x ) )` z ’ M ’{` " & Ž L n’
 ‘ M ’ & w ’ &  $ M $ & ’†  $ w e  3'Hš1 x ] + *3 ^ _) ) F  ^mx )_8„:=<>.0? xA@CB [ ) D  + UW   ¨ < 3U   *3 H Œ + ^ /)  8‡).0)  ~? ) U05(W ) H '0+ '3 ^  *3 H!"6 Œ q e )  ) U s q T Œ J  )  | 6A@76 qgq M ‘ & M ’'$ x | < F 6*1x*1/1
 x'101
h x1/101 )