Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval

Abstract

In this paper, based on the one-signed Green’s function and the compact results on the infinite interval, we obtain the existence and multiplicity of positive solutions for the boundary value problems $$\begin{cases} \Delta^2 x(n-1)-p(n)\Delta x(n-1)-q(n)x(n-1)+f(n,x(n))=0, &n\in\mathbb{N},\\  \alpha x(0)-\beta \Delta x(0)=0, & \lim\limits_{n\rightarrow\infty}x(n)=0  \end{cases}$$by the fixed point theorem in cones. The main results extend some results in the previous literature.