Multiplicity of solutions to an elliptic problem with singularity and measure data

Abstract

In this paper, we prove the existence of multiple nontrivial solutions of the following equation. \begin{align*} \begin{split} -\Delta_{p}u & = \frac{\lambda}{u^{\gamma}}+g(u)+\mu~\mbox{in}\,\,\Omega, u & = 0\,\, \mbox{on}\,\, \partial\Omega, u&>0 \,\,\mbox{in}\,\,\Omega, \end{split} \end{align*} where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain with $N \geq 3$, $1 < p-1 < q$ , $ \lambda>0$, $\gamma>0$, $g$ satisfies certain conditions, $\mu\geq 0$ is a bounded Radon measure.