﻿ 离散半正边值问题正解的存在性及多解性

# 离散半正边值问题正解的存在性及多解性Existence and Multiplicity of Semipositone Discrete Boundary Value Problems

Abstract: By using the Guo-Krasnosel’skii fixed point theorem, a Dirichlet boundary value problem with sign-changing nonlinearity is discussed and some results of existence and multiplicity of positive solutions are established.

[1] Berger, H. (2008) Existence of Nontrivial Solutions of a Two-Point Boundary Value Problem for a 2nth-Order Nonlinear Difference Equation. Advances in Dynamical Systems and Applications, 3, 131-146.

[2] Anderson, D. (2003) Discrete Third-Order Three-Point Right-Focal Boundary Value Problems. Computers & Mathematics with Applications, 45, 861-871.
http://dx.doi.org/10.1016/S0898-1221(03)80157-8

[3] Anderson, D. and Avery, R. (2001) Multiple Positive Solutions to a Third-Order Discrete Focal Boundary Value Problem. Computers & Mathematics with Applications, 42, 333-340.
http://dx.doi.org/10.1016/S0898-1221(01)00158-4

[4] Aykut, N. (2004) Existence of Positive Solutions for Boundary Value Problems of Second Order Functional Difference Equations. Computers & Ma-thematics with Applications, 48, 517-527.
http://dx.doi.org/10.1016/j.camwa.2003.10.007

[5] Bai, D. (2013) A Global Result for Discrete ϕ-Laplacian Ei-genvalue Problems. Advances in Difference Equations, 264, 10 p.

[6] Bai, D. and Xu, Y. (2007) Nontrivial Solutions of Boundary Value Problems of Second Order Difference Equations. Journal of Mathematical Analysis and Applications, 326, 297-302.
http://dx.doi.org/10.1016/j.jmaa.2006.02.091

[7] Bai, D. and Xu, X. (2013) Existence and Multiplicity of Difference ϕ-Laplacian Boundary Value Problems. Advances in Difference Equations, 267, 13 p.

[8] Ji, D. and Ge, W. (2008) Existence of Multiple Positive Solutions for Sturm-Liouville-Like Four-Point Boundary Value Problem with p-Laplacian. Nonlinear Analysis: Theory, Methods & Applications, 68, 2638-2646.
http://dx.doi.org/10.1016/j.na.2007.02.010

[9] Bai, D. and Xu, Y. (2008) Positive Solutions for Semipositone BVPs of Second-Order Difference Equations. Indian Journal of Pure and Applied Mathematics, 39, 59-68.

[10] Anuradha, V. and Shivaji, R. (1994) A Quadrature Method for Classes of Multi-Parameter Two Point Boundary Value Problems. Applicable Analysis, 54, 263-281.
http://dx.doi.org/10.1080/00036819408840282

[11] Anuradha, A. and Shivaji, R. (1996) Existence Results for Superlinear Semipositone BVP’s. Proceedings of the American Mathematical Society, 124, 757-763.
http://dx.doi.org/10.1090/S0002-9939-96-03256-X

[12] Feng, H. and Bai, D. (2011) Existence of Positive Solu-tions for Semipositone Multi-Point Boundary Value Problem. Mathematical and Computer Modelling, 54, 2287-2292.
http://dx.doi.org/10.1016/j.mcm.2011.05.037

[13] Anuradha, V. and Shivaji, R. (1999) Positive Solutions for a Class of Nonlinear Boundary Value Problems with Neumann-Robin Boundary Conditions. Journal of Mathematical Analysis and Applications, 236, 94-124.
http://dx.doi.org/10.1006/jmaa.1999.6439

[14] Bai, D. and Xu, Y. (2005) Existence of Positive Solutions for Boundary Value Problems of Second-Order Delay Differential Equations. Applied Mathematics Letters, 18, 621-630.
http://dx.doi.org/10.1016/j.aml.2004.07.022

[15] Bai, D. and Xu, Y. (2005) Positive Solutions of Second-Order Two-Delay Differential Systems with Twin-Parameter. Nonlinear Analysis, 63, 601-617.
http://dx.doi.org/10.1016/j.na.2005.05.021

[16] Castro, A. and Shivaji, R. (2000) Evolution of Positive Solution Curves in Semipositone Problems with Concave Nonlinearities. Journal of Mathematical Analysis and Applications, 245, 282-293.
http://dx.doi.org/10.1006/jmaa.2000.6787

[17] Hai, D. and Shivaji, R. (1998) Positive Solutions of Quasilinear Boundary Value Problems. Journal of Mathematical Analysis and Applications, 217, 672-686.
http://dx.doi.org/10.1006/jmaa.1997.5762

[18] Hai, D. and Shivaji, R. (2004) An Existence Result on Positive Solutions for a Class of p-Laplacian Systems. Nonlinear Analysis, 56, 1007-1010.
http://dx.doi.org/10.1016/j.na.2003.10.024

[19] Ma, R. (2003) Multiple Positive Solutions for a Semipositone Fourth-Order Boundary Value Problem. Hiroshima Mathematical Journal, 33, 217-227.

[20] Maya, C. and Shivaji, R. (1999) Multiple Positive Solutions for a Class of Semilinear Elliptic Boundary Value Problems. Nonlinear Analysis, 38, 497-504.
http://dx.doi.org/10.1016/S0362-546X(98)00211-9

[21] Sun, J. and Wei, J. (2008) Existence of Positive Solutions of Positive Solution for Semi-Positone Second-Order Three- Point Boundary-Value Problems. Electronic Journal of Differential Equations, 41, 1-7.

[22] Bai, D., Henderson, J. and Zeng, Y. (2015) Positive Solutions of Dis-crete Neumann Boundary Value Problems with Sign-Changing Nonlinearities. Boundary Value Problems, 1, 231.
http://dx.doi.org/10.1186/s13661-015-0500-8

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