Another approach on an elliptic equation of Kirchhoff type

Abstract

This paper is concerned with the existence of solutions to the class of nonlocal boundary value problems of the type

where $\Omega$ is a smooth bounded domain of ${\mathbb{R}}^N$ and $M$ is a positive continuous function. By assuming that $f(x,u)$ is a Carathéodory function which growths at most $|u{|}^{\frac{N}{N-2}}$, $N\ge 3$, and under a suitable growth condition on $M$, one proves an existence result by applying the Leray–Schauder fixed point theorem.