Existence result for an elliptic equation on locally finite graphs with singularity
Abstract
We study the following equation with singular nonlinearity on locally finite graphs $G=(V,E)$: $$\begin{aligned} \left \{ \begin{aligned} -\Delta u &=\frac{\lambda}{u^{\gamma}}+f(x,u) && \text{in }\Omega , \\ u &=0 \qquad &&\text{on }\partial \Omega , \end{aligned} \right . \end{aligned}$$ where Δ denotes the discrete Laplacian, V denotes the vertices set and E denotes the edges set, $0
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Boundary Value Problems
- Volume
- 2026
- Issue
- 1
- Publication date
- 9 February 2026
- Language
- EN