Nonexistence result for a semilinear elliptic problem

Salvador López-Martínez, Alexis Molino

Published 2019-02-23Version 1

In this paper we prove the nonexistence of nontrivial solution to \begin{equation*} \begin{cases} -\Delta u =f(u) &\text{in }\Omega, \\ u=0 &\text{on } \partial \Omega, \end{cases} \end{equation*} being $\Omega \subset \mathbb{R}^N$ ($N\geq 2$) a bounded domain with boundary smooth and $f$ Lispchitz with non-positive primitive.