Existence of multiple solutions to an elliptic problem with 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 & = λ|u|^{q-2}u+f(x,u)+μ\,\,\mbox{in}\,\,Ω, u & = 0\,\, \mbox{on}\,\, \partialΩ; \end{split} \end{align*} where $\Omega \subset {\mathbb{R}}^N$ is a smooth bounded domain with $N\ge 3$, $1<q^{\prime }<q<p-1;\lambda ,$ and $f$ satisfies certain conditions, $\mu >0$ is a Radon measure, $q^{\prime }=\frac{q}{q-1}$ is the conjugate of $q$.

References in corpus (1)

• Nonlinear elliptic equations with measures revisited