## Differential and Integral Equations

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

Antonio Azzollini

#### Abstract

In this paper we present a very simple proof of the existence of at least one nontrivial solution for a Kirchhoff-type equation on ${{\mathbb{R}^N}}$, 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.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 5/6 (2012), 543-554.

Dates
First available in Project Euclid: 20 December 2012

Azzollini, Antonio. The elliptic Kirchhoff equation in $\mathbb R^N$ perturbed by a local nonlinearity. Differential Integral Equations 25 (2012), no. 5/6, 543--554. https://projecteuclid.org/euclid.die/1356012678