(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we aim to investigate the difference equation ∆^2 y(t − 1) + |y(t)| = 0, t ∈ [1, T]_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 ∈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.