EXISTENCE RESULTS FOR POSITIVE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

Title & Authors
EXISTENCE RESULTS FOR POSITIVE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN
Liu, Yu-Ji;

Abstract
Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $\small{\LARGE\left\{{{\;{\Delta}[{\phi}({\Delta}x(n))]\;+\;f(n,\;x(n\;+\;1),{\Delta}x(n),{\Delta}x(n + 1))\;=\;0,\;n\;{\in}\;[0,N],}}\\{\;{x(0)-{\sum}^m_{i=1}{\alpha}_ix(n_i) = A,}}\\{\;{x(N+2)-\;{\sum}^m_{i=1}{\beta}_ix(n_i)\;=\;B.}}\right.}$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator $\small{{\Delta}}$x(n).
Keywords
one-dimension p-Laplacian difference equation;multi-point boundary value problem;positive solution;
Language
English
Cited by
1.
Global continuum of positive solutions for discrete p-Laplacian eigenvalue problems, Applications of Mathematics, 2015, 60, 4, 343
2.
Exact multiplicity of solutions for discrete second order Neumann boundary value problems, Boundary Value Problems, 2015, 2015, 1
3.
Existence of positive solutions for boundary value problems of p-Laplacian difference equations, Advances in Difference Equations, 2014, 2014, 1, 263
4.
Positive solutions of discrete Neumann boundary value problems with sign-changing nonlinearities, Boundary Value Problems, 2015, 2015, 1
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