Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval
Year: 2022
Author: Yanqiong Lu, Rui Wang
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 658–676
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.658
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 4 : pp. 658–676
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Positive solution Green’s function Compact Infinite interval.