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} -Δ_{p}u & = \fracλ{u^γ}+g(u)+μ~\mbox{in}\,\,Ω, u & = 0\,\, \mbox{on}\,\, \partialΩ, u&>0 \,\,\mbox{in}\,\,Ω, \end{split} \end{align*} where $\Omega \subset {\mathbb{R}}^N$ is a smooth bounded domain with $N\ge 3$, $1<p-1<q$ , $\lambda >0$, $\gamma >0$, $g$ satisfies certain conditions, $\mu \ge 0$ is a bounded Radon measure.

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