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.