Multiple solutions for a Kirchhoff-type equation with general nonlinearity

Abstract

This paper is devoted to the study of the following autonomous Kirchhoff-type equation $$-M\left({\int }_{{\mathbb{R}}^N}|\nabla u{|}^2\right)\Delta u=f(u),u\in H^1({\mathbb{R}}^N),$$ where $M$ is a continuous non-degenerate function and $N\ge 2$. Under suitable additional conditions on $M$ and general Berestycki-Lions type assumptions on the nonlinearity $f$, we establish several existence results of multiple solutions by variational methods, which are also naturally interpreted from a non-variational point of view.

18 pages, no figures. Minor modifications. Accepted for publication by Advances in Nonlinear Analysis and available online now as ahead of print

References in corpus (1)

• An autonomous Kirchhoff-type equation with general nonlinearity in ${\mathbb{R}}^N$

Cited by in corpus (2)

• Nonlinear scalar field equations with general nonlinearity
• An autonomous Kirchhoff-type equation with general nonlinearity in ${\mathbb{R}}^N$