Mathematica Eterna
Open Access

Abstract

Positive solutions for boundary value problems of the third-order q-symmetric difference equations with parameter

Qi GE, Chengmin HOU

In this paper, we study the existence and the nonexistence of positive solutions for boundary value problems of the third-order q-symmetric difference equations with parameter. By using the properties of the Green function and Guo-Krasnoselskii fixed point theorem on cones, we prove the existence of positive solutions to this equation when the parameter belongs to different interval. And by apagoge, we prove the nonexistence of positive solutions to this equation when the parameter belongs to different interval.