J. Nonl. Mod. Anal., 4 (2022), pp. 605-614.
Published online: 2022-06
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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.605}, url = {http://global-sci.org/intro/article_detail/jnma/20727.html} }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.