numerical solution of nonlinear boundary value problems

... positive solutions of dynamic equations on time scales (see, e.g., [1–7]) This work entails an extension of the paper by Chyan and Henderson [8] to eigenvalue problems for systems of nonlinear boundary ... problems, ” Journal of Mathematical Analysis and Applications, vol 208, no 1, pp 252–259, 1997 [14] L Hu and L Wang, “Multiple positive solutions of boundary value problems for systems of nonlinear second-order ... “Eigenvalues of some non-local boundary- value problems, ” Proceedings of the Edinburgh Mathematical Society, vol 46, no 1, pp 75–86, 2003 [19] G Infante and J R L Webb, “Loss of positivity in a nonlinear...

Ngày tải lên: 22/06/2014, 00:20

... positive solutions of dynamic equations on time scales (see, e.g., [1–7]) This work entails an extension of the paper by Chyan and Henderson [8] to eigenvalue problems for systems of nonlinear boundary ... problems, ” Journal of Mathematical Analysis and Applications, vol 208, no 1, pp 252–259, 1997 [14] L Hu and L Wang, “Multiple positive solutions of boundary value problems for systems of nonlinear second-order ... “Eigenvalues of some non-local boundary- value problems, ” Proceedings of the Edinburgh Mathematical Society, vol 46, no 1, pp 75–86, 2003 [19] G Infante and J R L Webb, “Loss of positivity in a nonlinear...

Ngày tải lên: 22/06/2014, 06:20

... “Existence of solution for a boundary value problem of fractional order,” Acta Mathematica Scientia B, vol 26, no 2, pp 220–228, 2006 S Zhang, “Positive solutions for boundary- value problems of nonlinear ... pair of order upper and lower solutions of 1.2 , then the boundary value problem 1.2 has at least one solution u t ∈ C3 0, , moreover, u t ≥u t ≥u t , t ∈ 0, 3.1 Boundary Value Problems Proof ... Sadarangani, “Existence and unqiueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems, ” Boundary Value Problems, vol 2009, Article ID 421310,...

Ngày tải lên: 21/06/2014, 07:20

... 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

... solutions of singular nonlinear m-point boundary value problems, Journal of Mathematical Analysis and Applications 284 (2003), no 2, 576–590 [7] R Ma and N Castaneda, Existence of solutions of ... of nonlinear m-point boundary- value problems, Journal of Mathematical Analysis and Applications 256 (2001), no 2, 556–567 [8] J R L Webb, Positive solutions of some three point boundary value problems ... un,λ (t) is a positive solution of (2.1λ ) The proof is complete n Proof of the main results Proof of Theorem 2.1 Let Λ = {λ ∈ (0,+∞)|(1.1λ ) has at least one positive solution} (3.1) By Lemma...

Ngày tải lên: 22/06/2014, 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

... 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,” Nonlinear ... Boundary Value Problems 13 Z Du, W Ge, and X Lin, “Existence of solutions for a class of third-order nonlinear boundary value problems, ” Journal of Mathematical Analysis and Applications, vol 294, no ... 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...

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

... Obviously, any positive C R -solution ψ of 3.8 satisfies 3.9 Moreover, one can show that these C R -solutions of 3.8 are in L1 R Therefore, the set of positive symmetric solutions to 3.9 which are ... only of interest to applications in mathematical physics but their functional analytic impact will speak for itself The results altogether show that solving the boundary value problems of Schrodinger ... an eigenvalue of X ∗ , hence the point spectrum of X ∗ is C According to the deficiency index structure 1, of the operator X, let us now choose the particular self-adjoint extension Y of X which...

Ngày tải lên: 21/06/2014, 20:20

... Therefore, u is the unique solution of PBVP (2.41) The proof of Lemma 2.7 is complete Lemma 2.8 u ∈ Ω is a solution of PBVP (1.1) if and only if u ∈ PC[JT , R] is solution of the following integral ... and v∗ are solutions of PBVP (1.1) in [u0 ,v0 ] Next we prove that u∗ and v∗ are the minimal and maximal solutions of PBVP (1.1) in [u0 ,v0 ] In fact, let w ∈ [u0 ,v0 ] be a solution of PBVP(1.1), ... vol 18, no 1-2, pp 18–56, 1990 [4] J Henderson, “Double solutions of impulsive dynamic boundary value problems on a time scale,” Journal of Difference Equations and Applications, vol 8, no 4, pp...

Ngày tải lên: 22/06/2014, 19:20

... Nonlocal boundary value problems of the first kind for a SturmLiouville operator in its differential and finite difference aspects, Differ Equ 23 (1987), no 7, 803–810 , Nonlocal boundary value problems of ... with boundary conditions (2.3) P j h has a generalized zero at n − ( j + 2) because of the boundary conditions In addition, because of the nonlocal boundary conditions and repeated applications of ... 0, s ∈ {0, ,b − n} (2.17) Proof The proof requires only a simple extension from the proof of Theorem 2.3 As summarized in the fourth paragraph of the proof of Theorem 2.3, we know that P1 G has...

Ngày tải lên: 23/06/2014, 00:20

... smooth boundary of Ω, ν is the outward normal to Γ and a is a positive number The solvability and smoothness of the solution of problem (1) follows from the general theory of elliptic problems ... defined on pairs of boundary functions w0 and domain functions ϕ z= w0 ϕ by the formula Bz = −a ∂u ∂ν , ϕ − au (5) Boundary- Operator Method for Approximate Solution of Boundary Value Problem 11 ... (13) Boundary- Operator Method for Approximate Solution of Boundary Value Problem 13 u being defined from (6) The complete continuity of B0 is easily followed from the embedding theorems of Sobolev...

Ngày tải lên: 06/08/2014, 05:20

... CHAPTER TWO Singular Boundary Value Problems for Difference Equations This chapter is devoted to the study of solutions of singular boundary value problems for difference equations of the form, (−1)n ... the least of which is this dissertation Thanks! v CHAPTER ONE Introduction In this dissertation we will be concerned with the existence of positive solutions of singular boundary value problems ... by looking for solutions u of singular discrete boundary value problems of the form, (−1)n ∆n u(t−(n−1))+f (t, u(t), , ∆n−1 u(t−(n−1))) = 0, t ∈ [n−1, T +1], (1.1) satisfying boundary conditions,...

Ngày tải lên: 13/11/2014, 09:09

... 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 ... Existence of positive solutions for nonlinear m-point boundary value problems on time scales Junfang Zhao∗1 , Hairong Lian1 and Weigao Ge2 School of Mathematics and Physics, China University of Geosciences,...

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 ... 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 ... 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...

Ngày tải lên: 20/06/2014, 22:20

... 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 ... 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, ... 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...

Ngày tải lên: 21/06/2014, 11:20

... 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 value problems ... 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 ... exists a bounded monotone sequence of solutions of linear problems that Advances in Difference Equations converges uniformly and quadratically to a solution of the nonlinear original problem If ∂2...

Ngày tải lên: 21/06/2014, 16:20

... 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 ... Existence of positive solutions for nonlinear m-point boundary value problems on time scales Junfang Zhao∗1 , Hairong Lian1 and Weigao Ge2 School of Mathematics and Physics, China University of Geosciences,...

Ngày tải lên: 21/06/2014, 17:20

... 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 ... Existence of positive solutions for nonlinear m-point boundary value problems on time scales Junfang Zhao∗1 , Hairong Lian1 and Weigao Ge2 School of Mathematics and Physics, China University of Geosciences,...

Ngày tải lên: 21/06/2014, 17:20