Year: 2022
Author: Huijuan Li, Gaofeng Du, Cunyan Yue
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 3 : pp. 605–614
Abstract
In this paper, we aim to investigate the difference equation $$∆^2 y(t − 1) + |y(t)| = 0, t ∈ [1, T]_{\mathbb{Z}}$$ with different boundary conditions $y(0) = 0$ or $∆y(0) = 0$ and $y(T + 1) = B$ or $∆y(T) = B,$ where $T ≥ 1$ is an integer and $B ∈\mathbb{R}.$ We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.605
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 3 : pp. 605–614
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Second-order difference equation Different boundary conditions Boundary value problems.