... considering the effects ofthe changes in the length ofthe strings during the vibrations The parameters in (1 .3) have the following meanings: L is the length ofthe string, h is the area of cross-section, ... Kirchhoff type, Nonlinear Analysis Theory, Methods & Applications 63 (2005), no 5 7, e19 67 e1 977 [ 17] J Moser, A new proof of De Giorgi’s theorem concerning the regularity problem for elliptic differential ... degenerate parabolic equation with a nonlocal source, Journal of Mathematical Analysis and Applications 264 (2001), no 2, 577 –5 97 [12] W Deng, Y Li, and C Xie, Existence and nonexistence of global...
... (19 83) , no 3, 233 –245 G Yuan, The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities, Memoirs ofthe American Mathematical Society, vol 132 , American Mathematical ... ⊃ Kφ Therefore, we have the / conclusion Remarks 3.3 (1) In case Φ = φ, Corollary 3. 2 reduces to Theorem3. 1 (2) Urai (see [12, Theoremforthe case (K∗ )]) obtained Corollary 3. 2 under the restriction ... York, 19 87, pp 235 –244 P W Sy and S Park, The KKM maps and fixed point theorems in convex spaces, Tamkang J Math 34 (20 03) , no 2, 169– 174 K Urai, Fixed point theorems and theexistenceof economic...
... c, Bộ ba số sau ba cạnh tam giác: A 4cm; 4cm; 9cm B 3cm; 4cm; 6cm C 3cm; 4cm; 8cm d, Cho tam giác MNP có góc M 30 ; góc P 130 0 Quan hệ độ dài 3cạnh tam giác là: A MN > MP > NP B MP > MN > NP C ... sau ba cạnh tam giác: A 1cm; 2cm; 5cm B 4cm; 5cm; 8cm C 2cm; 7cm; 10 cm d, Cho tam giác ABC có góc A 50 ; góc B 70 0 Quan hệ độ dài 3cạnh tam giác là: A BC > AB > AC B AB > AC > BC C AC > AB > ... nghiệm( 3 iểm): Câu 1: Viết vào làm chữ in hoa đứng trước câu trả lời đúng: a, Bộ ba số sau ba cạnh tam giác: A 4cm; 4cm; 9cm B 3cm; 4cm; 6cm C 3cm; 4cm; 8cm b, Cho tam giác MNP có góc M 30 ; góc...
... not examined This report begins with an overview ofthe forms of insurance offered within the industry, in order to gain an understanding ofthe market It is then followed by an analysis of underwriting ... phase ofthe cycle can increase the steepness (increase combined ratio) ofthe cycle by reducing the demand for insurance The industry’s increased capacity together with the reduced demand leads ... factors other than the present value of expected losses Therefore, one cannot test the theories against each other, nor can a single theory explain the cause of underwriting cycles (Meier and Outreville...
... evidence fortheexistenceof things whose existence is at least genuinely possible And the provision of just such a conception is one ofthe principal tasks of metaphysics .3 The point of these remarks ... more credibility to the extent that it is consistent with the other METAPHYSICS AND THE PHILOSOPHY OF MIND The philosophy of mind is not only concerned with the philosophical analysis of mental ... general conception ofthe whole of reality, we cannot hope to render compatible the theories and observations ofthe various different sciences: and providing that conception is not the task of...
... 32 37 29 34 1.8 0 .3 ´ 1 03 3.8 0 .7 ´ 1 03 0.9 0.2 ´ 1 03 71 32 152 10 8.5 19 10 8 .3 1.5 ´ 1 03 1 .7 0.4 ´ 1 03 15.2 2.5 ´ 1 03 16 18 0.9 0.2 ´ 1 03 96 7 1 13. 7 ... 0 .3 mM) (Table 1) The binding ofthe ®rst CN± ligand to the iron was thus more easy in the hydrophobic binding pocket ofthe antibody than the binding ofthe second one, most probably because of ... binding of ligands on the iron of Fe(porphyrin))13G10 complexes: (A) binding of H2O2 on the iron of 13G10-(Fe(ToCPP), (B) binding of two CN± ligands on the iron of 13G10-(Fe(ToCPP), (C) binding of...
... functional-type cone expansion compression fixed-point theorem, the author gets theexistenceof at least one positive solution to BVP (1 .3) , (1.4) and BVP (1 .3) , (1.5) However, to the best ofthe authors’ ... e s s 1 /3 es s h(τ ) τ ∆s ξi 1 /3 T φq h(s) s + i=1 ξ1 βi φq 1 /3 es s +3 ∆s s 1 /3 1 /3 ∆s 3 = 3( e + e2 − 1)1 /3 + 2(e + e2 − e1/2 )1 /3 + 3e2 /3 + (e + e2 − 1)4 /3 − (e + e2 − e1/2 )4 /3 4 ≈ 17. 5216 ... u) > 23. 2 37 5 = (50/ 17. 5216 )3 = φp (ν/D), for t ∈ [1/2, 2], u ∈ [50, 200]; (iii) f (t, u) < 70 27 .30 5 = (400/20.8 832 )3 = φp (g/R), for t ∈ [0, 2], u ∈ [0, 400] Thus, if all the conditions in Theorem...
... Corollaries 3. 1 and 3. 2 all generalize and improve [5, Theorem3. 4] and the primitive Chatterjea’s fixed point theorem [3] Fixed point theorems of generalized Kannan’s type and others The following ... assumptions of Corollary 3. 2 are satisfied Let g:= max {a, b} Then γ ∈ [0, ) and (3. 14) implies (3. 15), and the conclusion of Corollary 3.3 follows from Corollary 3. 2 (b) Theorems 3. 1 -3. 4 and Corollaries ... below) and MT -functions to extend Berinde-Berinde’s fixed point theorem In [5], some generalizations of Kannan’s fixed point theorem, Chatterjea’s fixed point theorem and other new fixed point theorems...
... I, s Î I The proof is complete Similar to the proof ofTheorem3. 1, we can prove the following results Theorem3. 2 Assume that (H) holds, P is normal and for any x Î P, A(f)0 >Bf∞ Then problem ... Applying (a) of Lemma 1.1 to (3. 3) and (3. 4) yields that T has a fixed point ∈ Kr3 ,r4 , r3 ≤ x∗ c ≤ r4 and x*(t) ≤ e(t)x*(s) >θ, t Î I, s Î I The proof is complete Theorem3.3 Assume that (H) ... ≤ x c Zhang Fixed Point Theory and Applications 2011, 2011: 43 http://www.fixedpointtheoryandapplications.com/content/2011/1/ 43 Page of Therefore, Tx c ≤ x c, t ∈ I, x ∈ K, x c = r1 Next, turning...
... Nonlinear Analysis Theory, Methods & Applications, vol 69, no 4, pp 136 4– 1 37 5, 2008 13 Q L Yao and Z B Bai, Existenceof positive solutions of a BVP for u4 t − λh t f u t 0,” Chinese Annals of ... no 11026060 , and nwnu-kjcxgc 03- 69, 03- 61 References Z Bai, The method of lower and upper solutions for a bending ofan elastic beam equation,” Journal of Mathematical Analysis and Applications, ... 1/4≤t 3/ 4 Th t ≥ d1 Th , max 1/4≤t 3/ 4 Th t ≤− d2 ξ C2 Th ≤ 0, u ∈ 3. 13 Fixed Point Theory and Applications By 3.7 and 3. 10 , 1/4≤t 3/ 4 max 1/4≤t 3/ 4 Qu t ≥ TFu t ≥ d1 TFu TFu t ≤− 1/4≤t 3/ 4 t...
... means In Section 3, we give the proof of positive semidefiniteness of matrices generated by the difference of that inequality obtained from the generalization of Mitrinovi´ -Peˇ ari´ inequality and ... organized in this manner In Section 2, we give the generalization of Mitrinovi´ -Peˇ ari´ inequality and prove the mean value theorems of Cauchy type We c c c also introduce the new type of Cauchy ... Then the statement ofTheorem3. 2 with t b dx − instead of r x ϕt a t α Da u1 x α Da u2 x dx 3. 13 is valid In the following theorem, we prove the monotonicity property of Ms,t defined in 2.52 Theorem...
... solution The proof is complete Proof ofTheorem 1.2 In the proof ofTheorem 1.1, the condition that F2 n, x ≥ for n, x ∈ J × R, |x| ≤ in F1 , is only used in thethe proofs of assumption ii of Lemma ... that there exists k0 ∈ N such that Π f n, uk n n −Π − f n, u0 n |uk n − u0 n | < ε, for k ≥ k0 3. 36 16 Advances in Difference Equations On the other hand, it follows from 3. 31 , 3. 33 , 3. 34 , 3. 35 ... Ma and Z Guo, “Homoclinic orbits and subharmonics for nonlinear second order difference equations,” Nonlinear Analysis: Theory, Methods & Applications, vol 67, no 6, pp 1 73 7 – 174 5, 20 07 13 M Ma and...
... functional-type cone expansion compression fixed-point theorem, the author gets theexistenceof at least one positive solution to BVP (1 .3) , (1.4) and BVP (1 .3) , (1.5) However, to the best ofthe authors’ ... e s s 1 /3 es s h(τ ) τ ∆s ξi 1 /3 T φq h(s) s + i=1 ξ1 βi φq 1 /3 es s +3 ∆s s 1 /3 1 /3 ∆s 3 = 3( e + e2 − 1)1 /3 + 2(e + e2 − e1/2 )1 /3 + 3e2 /3 + (e + e2 − 1)4 /3 − (e + e2 − e1/2 )4 /3 4 ≈ 17. 5216 ... u) > 23. 2 37 5 = (50/ 17. 5216 )3 = φp (ν/D), for t ∈ [1/2, 2], u ∈ [50, 200]; (iii) f (t, u) < 70 27 .30 5 = (400/20.8 832 )3 = φp (g/R), for t ∈ [0, 2], u ∈ [0, 400] Thus, if all the conditions in Theorem...
... functional-type cone expansion compression fixed-point theorem, the author gets theexistenceof at least one positive solution to BVP (1 .3) , (1.4) and BVP (1 .3) , (1.5) However, to the best ofthe authors’ ... e s s 1 /3 es s h(τ ) τ ∆s ξi 1 /3 T φq h(s) s + i=1 ξ1 βi φq 1 /3 es s +3 ∆s s 1 /3 1 /3 ∆s 3 = 3( e + e2 − 1)1 /3 + 2(e + e2 − e1/2 )1 /3 + 3e2 /3 + (e + e2 − 1)4 /3 − (e + e2 − e1/2 )4 /3 4 ≈ 17. 5216 ... u) > 23. 2 37 5 = (50/ 17. 5216 )3 = φp (ν/D), for t ∈ [1/2, 2], u ∈ [50, 200]; (iii) f (t, u) < 70 27 .30 5 = (400/20.8 832 )3 = φp (g/R), for t ∈ [0, 2], u ∈ [0, 400] Thus, if all the conditions in Theorem...
... Acknowledgments The author is very grateful to Editor ofthe Journal and the anonymous referees for their carefully reading ofthe first draft ofthe manuscript and making many valuable suggestions 22 and ... Nonlinear Anal 30 (6), 536 9– 5 37 4 (19 97) [2] Feng, W, Webb, JRL: Solvability of a m-point boundary value problems with nonlinear growth J Math Anal Appl 212, 4 67 480 (19 97) [3] Gupta, CP: A generalized ... modified The plan ofthe article is as follows Section contains a number of lemmas useful to the derivation ofthe main results The proof ofthe main results will be stated in Section A class of examples...
... the method of proving Theorems 3. 1 and 3. 2, we can deduce the conclusion easily, so we omit it here Theorem3. 12 Suppose that i0 2, i∞ 0, and the condition C4 ofTheorem3. 2 hold Then BVP 1.4 ... Then BVP 1.4 has at least one ∞, similar to the second part ofTheorem3. 1, we have Au ≥ u for Proof Since f0 u ∈ P ∩ ∂ΩH3 By f∞ ∈ 0, ϕp A1 , similar to the second part of proof ofTheorem3. 4, ... least one positive solution ∞ and the condition C3 in Theorem3. 2 hold Then BVP 1.4 Corollary 3. 10 Suppose that f0 has at least one positive solution ∞ and the condition C3 in Theorem3. 2 hold Then...
... Corollary 3. 5 Let Ω be bounded and p0 ∈ H 1,r Ω There is a weak solution pθ ∈ H0 Ω 3. 1 in the sense of Definition 3. 1 p0 to Proof ofTheorem3. 2 Theexistence result is given in Corollary 3. 5, and ... equation 1.6 Therefore, arguments after 11, equation 3. 19 can be used to complete the proof ofTheorem 4.2 Acknowledgments The project is partially supported by NSF/STARS Grant NSF-02 079 71 and Research ... p to the nonlinear equation 1 .3 In Section 4, we study theexistenceof weak solutions to Problem Using Rothe’s method of time discretization and anexistence result for Problem 1, one can establish...