Volume 4, Issue 4
Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval

J. Nonl. Mod. Anal., 4 (2022), pp. 658-676.

Published online: 2023-08

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• 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.

34B15, 34B18, 34B40

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@Article{JNMA-4-658, author = {Lu , Yanqiong and Wang , Rui}, title = {Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {4}, number = {4}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.658}, url = {http://global-sci.org/intro/article_detail/jnma/21904.html} }
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 -

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.

Yanqiong Lu & Rui Wang. (2023). Positive Solutions of Second-Order Difference Equation with Variable Coefficient on the Infinite Interval. Journal of Nonlinear Modeling and Analysis. 4 (4). 658-676. doi:10.12150/jnma.2022.658
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