# Nonexistence result for a semilinear elliptic problem

## TL;DR

This paper establishes conditions under which no nontrivial solutions exist for a class of semilinear elliptic boundary value problems, specifically when the nonlinearity has a non-positive primitive.

## Contribution

It provides a nonexistence theorem for solutions of semilinear elliptic equations with certain nonlinearities and boundary conditions.

## Key findings

- Proves nonexistence of solutions under specified conditions.
- Extends understanding of solution behavior for elliptic problems.
- Applicable to bounded domains with particular nonlinearities.

## Abstract

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 $\Omega \subset \mathbb{R}^N$ ($N\in \mathbb{N}$) a bounded domain and $f$ locally Lispchitz with non-positive primitive.