TY - JOUR
T1 - Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval
AU - Lu , Yanqiong
AU - Wang , Rui
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 658
EP - 676
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.658
UR - https://global-sci.org/intro/article_detail/jnma/21904.html
KW - Positive solution, Green’s function, Compact, Infinite interval.
AB - <p style="text-align: justify;">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 $$\begin{cases} \Delta^2 x(n-1)-p(n)\Delta x(n-1)-q(n)x(n-1)+f(n,x(n))=0, &amp;n\in\mathbb{N},\\&nbsp; \alpha x(0)-\beta \Delta x(0)=0, &amp; \lim\limits_{n\rightarrow\infty}x(n)=0&nbsp; \end{cases}$$by the fixed point theorem in cones. The main results extend some results in
the previous literature.</p>