Positive solutions for second-order singular difference equation with nonlinear boundary conditions. (English) Zbl 1524.39030
Summary: In this paper, we discuss the existence of positive solutions for the second-order singular difference equation boundary value problem
\[
\begin{cases}
-\Delta^2 u(t-1) = \lambda g(t)f(u), &t\in[1, T]_{\mathbb{Z}},\\
u(0) = 0,\\
\Delta u(T) + c(u(T+1))u(T+1) = 0,
\end{cases}
\]
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.
MSC:
| 39A27 | Boundary value problems for difference equations |
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