solution of boundary value problems

... Page of 18 problems with integral boundary conditions constitute a very interesting and important class of problems They include two-point, three-point, multipoint and nonlocal boundary value problems ... existence of solutions for boundary value problems with integral boundary conditions on time scales Motivated by the statements above, in this paper, we are concerned with the following boundary value ... Positive solutions of a three-point boundary- value problem on a time scale Elec J Differ Equ 2003(82), 1–11 (2003) Khan, RA, Nieto, JJ, Otero-Espinar, V: Existence and approximation of solution of...

Ngày tải lên: 20/06/2014, 22:20

... of positive solutions of singular superlinear boundary value problems, ” Acta Mathematica Sinica, vol 48, no 1, pp 25–34, 2005 (Chinese) [8] Z L Wei, “Positive solutions to singular boundary value ... C [0,1] is a solution of BVP (3.1) if (x, y) satisfies (3.1) Moreover, we call that (x, y) is a positive solution of BVP (3.1) if x(t) > 0, y(t) > 0, t ∈ (0,1) 10 Boundary Value Problems To prove ... using the similar methods of our proof, we can show that SBVP (2.47) has the similar conclusions of Theorems 2.3–2.5 Continuous case We consider boundary value problems of system for nonlinear...

Ngày tải lên: 22/06/2014, 22:20

... uniqueness of solutions to boundary value problems on time scales,” Advances in Difference Equations, vol 2004, no 2, pp 93–109, 2004 12 C C Tisdell and H B Thompson, “On the existence of solutions to boundary ... purpose of this paper is to develop the method of upper and lower solutions and the method of quasilinearization 22–26 Under suitable conditions on f, we obtain a monotone sequence of solutions of ... quadratically to a unique solution of the BVP 1.1 Proof Conditions A1 and A2 ensure the existence of a unique solution x of the BVP 1.1 such that α t ≤x t ≤β t , t ∈ 0, σ 3.5 T In view of 3.4 , we have...

Ngày tải lên: 21/06/2014, 16:20

... transversality and boundary value problems on time scales,” Journal of Mathematical Analysis and Applications, vol 289, no 1, pp 110–125, 2004 26 Z He, “Existence of two solutions of m-point boundary value ... focal boundary value problems on a measure chain,” Applied Mathematics Letters, vol 18, no 1, pp 41–47, 2005 20 M Feng, X Zhang, and W Ge, “Positive solutions for a class of boundary value problems ... Nieto, and V Otero-Espinar, “Existence and approximation of solution of three-point boundary value problems on time scales,” Journal of Difference Equations and Applications, vol 14, no 7, pp...

Ngày tải lên: 21/06/2014, 20:20

... interval boundary value problem, Annali di Matematica Pura ed Applicata Serie Quarta 176 (1999), 379–394 [12] R Ma, Existence of positive solutions for second-order boundary value problems on infinity ... PC [0,n] is a solution of (2.9) if and only if y is a fixed point of the equation y = Ln −1 F y (2.13) We apply the Leray-Schauder continuation theorem to obtain the existence of a solution for ... alternative of Leray-Schauder type [7] guarantees that (Ln )−1 N has a fixed point, that is, (2.9) has a solution yn ∈ PC [0,n], and ≤ yn ≤ M, ≤ yn ≤ M The other proof is similar to the proof of Theorem...

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 31/03/2014, 15:23

... structure of the set of positive solutions of (1.1), (1.2), and obtain the existence of positive solutions of (1.1) and (1.2) Moreover, we can also obtain the existence of negative solutions of (1.1) ... definition of a positive solution and a negative solution of (1.1) and (1.2) Definition 1.1 A positive solution of problem (1.1) and (1.2) refers to a pair (r, u), where r ≠ 0, u is a solution of (1.1) ... characteristic value of T if there exists v Ỵ E, v ≠ 0, such that v = μTv, i.e., μ-1 is a nonzero eigenvalue of T Let r(T) denote the set of real characteristic values of T and Γ denote the closure of the...

Ngày tải lên: 20/06/2014, 20:20

... Kaufmann, ER: Positive solutions of a three-point boundary value problem on a time scale Electron J Diff Equ 82, 1–11 (2003) 11 Chyan, CJ, Henderson, J: Twin solutions of boundary value problems for differential ... composed of N parts of different densities can be set up as a multi-point boundary value problem [3] Many problems in the theory of elastic stability can be handled by the method of multi-point problems ... positive solutions of three-point boundary value problems for p-Laplacian dynamic equations J Comput Appl Math 206, 967–976 (2007) 17 Graef, J, Kong, L: First-order singular boundary value problems...

Ngày tải lên: 20/06/2014, 20:20

... are lower and upper solutions of (1.1-1.2), respectively Alsaedi and Aqlan Boundary Value Problems 2011, 2011:47 http://www.boundaryvalueproblems.com/content/2011/1/47 Page of 11 (A2) N Ỵ C[J ... Alsaedi and Aqlan Boundary Value Problems 2011, 2011:47 http://www.boundaryvalueproblems.com/content/2011/1/47 Page of 11 success at analyzing and predicting the onset of chaos in speech and ... and Aqlan: On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms Boundary Value Problems 2011 2011:47 Page 11 of 11 ...

Ngày tải lên: 20/06/2014, 22:20

... Caballero et al Boundary Value Problems 2011, 2011:25 http://www.boundaryvalueproblems.com/content/2011/1/25 Page of and they proved the existence of positive solutions by means of the Krasnosel’skii ... Caballero et al.: On existence and uniqueness of positive solutions to a class of fractional boundary value problems Boundary Value Problems 2011 2011:25 Page of ... uniqueness of the solution gives us x(t) = The reverse implication is obvious Caballero et al Boundary Value Problems 2011, 2011:25 http://www.boundaryvalueproblems.com/content/2011/1/25 Page of Remark...

Ngày tải lên: 20/06/2014, 22:20

... Caballero et al Boundary Value Problems 2011, 2011:25 http://www.boundaryvalueproblems.com/content/2011/1/25 Page of and they proved the existence of positive solutions by means of the Krasnosel’skii ... Caballero et al.: On existence and uniqueness of positive solutions to a class of fractional boundary value problems Boundary Value Problems 2011 2011:25 Page of ... uniqueness of the solution gives us x(t) = The reverse implication is obvious Caballero et al Boundary Value Problems 2011, 2011:25 http://www.boundaryvalueproblems.com/content/2011/1/25 Page of Remark...

Ngày tải lên: 21/06/2014, 00:20

... positive solution of (2) (9) Zhong and An Boundary Value Problems 2011, 2011:8 http://www.boundaryvalueproblems.com/content/2011/1/8 Page of Remark Theorem contains the partial results of [4-7] ... G- are the positive and negative parts of G Zhong and An Boundary Value Problems 2011, 2011:8 http://www.boundaryvalueproblems.com/content/2011/1/8 Page of We denote σ = ρ maxt,s∈[0,T] G(t, s) ... this article as: Zhong and An: Existence of positive solutions to periodic boundary value problems with sign-changing Green’s function Boundary Value Problems 2011 2011:8 ...

Ngày tải lên: 21/06/2014, 01:20

... where y, z ∈ P and y ≤ τ x , z ≤τ x Boundary Value Problems 3 Singular Third-Order Boundary Value Problem This section discusses singular third-order boundary value problem 1.1 Let P {x ∈ C I ... nonhomogeneous boundary value problems, ” Applied Mathematics Letters, vol 22, no 1, pp 45–51, 2009 J R Graef and J R L Webb, “Third order boundary value problems with nonlocal boundary conditions,” ... “Positive solutions of singular third-order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol 306, no 2, pp 589–603, 2005 10 Boundary Value Problems 13 Z...

Ngày tải lên: 21/06/2014, 05:20

... critical point of mountain pass type of J, then x is a critical point of mountain pass type of J Proof of Theorem 1.3 In this section, firstly, we obtain a positive solution u and a negative solution ... sign-changing solutions, ii k is even and 1.1 has six solutions, three of which are of the same sign, iii k is odd and 1.1 has two sigh-changing solutions, iv k is odd and 1.1 has three solutions of the ... points and no other critical points, then d J , Σ1 , −1 3.49 Boundary Value Problems 17 Now, we can give the proof of Theorem 1.3 Proof of Theorem 1.3 The functional J satisfies 2.18 in Lemma 2.10...

Ngày tải lên: 21/06/2014, 05:20

... dynamic boundary value problems with mixed derivatives,” Advances in Difference Equations, vol 2006, Article ID 54989, 15 pages, 2006 C J Chyan and J Henderson, “Twin solutions of boundary value problems ... scales,” Boundary Value Problems, vol 2011, Article ID 198598, 15 pages, 2011 12 J Henderson, “Multiple solutions for 2m order Sturm-Liouville boundary value problems on a measure chain,” Journal of ... independent of λ ∈ 0, , such that x < C for each solution x t to the boundary value problem xΔΔ t λf t, xσ t , xΔ t , xΔ a 0, t ∈ a, ρ2 b Ì, x b Then the boundary value problem 1.2 has at least one solution...

Ngày tải lên: 21/06/2014, 05:20

... eigenfunctions of the original boundary value problems – to eigenfunctions of the corresponding transformed boundary value problems In particular, if λ1 , , λs l m are the eigenvalues of one of the ... eigenvalue, one less eigenvalue, or the same number of eigenvalues as the original boundary value problem Thus, it is possible to construct a chain, or hierarchy, of difference boundary value problems ... to eigenfunctions of the corresponding transformed boundary value problems In particular, if λ0 , λ1 , , λs l m are the eigenvalues of one of the original boundary value problems, 10 – 12...

Ngày tải lên: 21/06/2014, 07:20

... multiple solutions of Lidstone boundary value problems, ” Acta Mathematica Hungarica, vol 86, no 1-2, pp 137–168, 2000 Y.-R Yang and S S Cheng, “Positive solutions of a Lidstone boundary value problem ... for a.e t ∈ J, then x is called a solution of 2.8 2.8 Boundary Value Problems Auxiliary Regular Problems Let j ∈ Ỉ and denote by Gj t, s the Green function of the problem x 2j t x 2i 0, x 2i ... t ∈ J, ≤ j ≤ m − 3.9 Boundary Value Problems 0, It is easy to check that x ∈ AC2m J is a solution of problem 2.8 , 1.2 if and only if x and its derivative x is a solution of a problem involving...

Ngày tải lên: 21/06/2014, 11:20

... existence of positive solutions of nonlinear periodic boundary value problem x x f t, x , x T , t ∈ 0, T , x x T , where f : 0, × R → R is satisfying Carath´ odory conditions e 3.1 Boundary Value Problems ... existence of positive solutions of 3.17 will not be guaranteed in this case Proof of Theorem 3.2 We only prove i ii can be proved by a similar method To study the existence of positive solutions of ... t, s , 0≤t,s≤T m: G t, s 0≤t,s≤T 2.19 Boundary Value Problems Finally, we state a result concerning the global structure of the set of positive solutions of parameterized nonlinear operator equations,...

Ngày tải lên: 21/06/2014, 11:20

... 2.36 has a unique solution c1 c2 Therefore v t ≡ w t for t ∈ −τ, T This completes the proof of the uniqueness of the solution 10 Boundary Value Problems Existence of Positive Solutions In this ... Shi, and D C Zhang, “Existence of positive solutions for boundary value problems of nonlinear functional difference equation with p-Laplacian operator,” Boundary Value Problems, vol 2007, Article ... Gai, Boundary value problems for functional differential systems,” Indian Journal of Pure and Applied Mathematics, vol 36, no 12, pp 685–705, 2005 X Deng and H Shi, “On boundary value problems...

Ngày tải lên: 21/06/2014, 11:20

... behavior of the components for the second order m-point boundary value problems, ” Boundary Value Problems, vol 2008, Article ID 254593, 10 pages, 2008 R Ma and Y An, “Global structure of positive solutions ... m-point boundary- value problems, ” Electronic Journal of Differential Equations, vol 2004, no 89, pp 1–14, 2004 S Jingxian, X Xian, and D O’Regan, “Nodal solutions for m-point boundary value problems ... the global structure of positive solutions of 1.1 , 1.2 with f0 ∞ However, to the best of our knowledge, there is no paper to discuss the global structure of nodal solutions of 1.1 , 1.2 with f0...

Ngày tải lên: 21/06/2014, 11:20