Positive solutions of a discrete nonlinear third-order three-point eigenvalue problem with sign-changing Green's function

Abstract

In this paper, we discuss the existence of positive solutions to a discrete third-order three-point boundary value problem. Here, the weight function a(t)a\left(t) and the Green function G(t,s)G\left(t,s) both change their sign. Despite this, we also obtain several existence results of positive solutions by using the Guo-Krasnoselskii’s fixed-point theorem in a cone.

Keywords

• third-order difference equation
• three-point boundary conditions
• sign-changing green’s function
• guo-krasnoselskii’s fixed-point theorem
• positive solutions
• 39a10
• 39a12