Positive Solutions for SecondOrder 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). 

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Abstract: 
In this paper, we discuss the existence of positive solutions for the secondorder singular difference equation boundary value problem $$\left\{\begin{array}{ll}\Delta^{2} u(t1)=\lambda g(t)f(u), &t\in [1,T]_\mathbb{Z},\\u(0)=0,\\ \Delta u(T)+c(u(T+1))u(T+1)=0,\end{array}\right.$$ 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:20952651.2023.01.011 
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