The elliptic Kirchhoff equation in ${\mathbb{R}}^N$ perturbed by a local nonlinearity

Abstract

In this paper we present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\RN$, for $N\ge 3$. In particular, in the first part of the paper we are interested in studying the existence of a positive solution to the elliptic Kirchhoff equation under the effect of a nonlinearity satisfying the general Berestycki-Lions assumptions. In the second part we look for ground states using minimizing arguments on a suitable natural constraint.

arXiv comment11 pages

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• An autonomous Kirchhoff-type equation with general nonlinearity in ${\mathbb{R}}^N$
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• On the Kirchhoff equation with prescribed mass and general nonlinearities
• Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness