Existence of positive solutions for a class of nonlinear elliptic equations with Hardy potential
Abstract
This paper is concerned with a class of nonlinear elliptic equations with a generalized Hardy potential$ \begin{equation*} -\Delta u = \frac{\lambda }{|x{{|}^{\alpha }}}u-b(x)g(u), \ x\in \Omega \backslash \{0\}, \end{equation*} $where $ \alpha > 0 $, $ \Omega \subset {\ \mathbb{R}}^{N}(N\geq 3) $ is a bounded smooth domain containing the origin. We establish the existence, nonexistence, and asymptotic behavior of positive solutions. When the potential function $ |x|{^{-\alpha }} $ has strong singularity at the origin, we obtain some qualitative properties of positive solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- AIMS Mathematics
- Volume
- 11
- Issue
- 2
- Pages
- 3441–3463
- Publication date
- 1 January 2026