Positive Solutions for Second-Order Singular Difference Equation with Nonlinear Boundary Conditions
Received:February 28, 2022  Revised:August 19, 2022
Key Words: difference equation   nonlinear boundary conditions   positive solutions
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11961060).
 Author Name Affiliation Huijuan LI Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China Alhussein MOHAMED Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China Chenghua GAO Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China
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Abstract:
In this paper, we discuss the existence of positive solutions for the second-order singular difference equation boundary value problem $$\left\{\begin{array}{ll}-\Delta^{2} u(t-1)=\lambda g(t)f(u), &t\in [1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{array}\right.$$ where $\lambda>0$ is a positive parameter, $f:(0,\infty)\rightarrow \mathbb{R}$ is continuous, and is allowed to be singular at $0$. The existence of positive solutions is established via introducing a new complete continuous operator.
Citation:
DOI:10.3770/j.issn:2095-2651.2023.01.011
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