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arXiv · 1001.0269

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

Antonio Azzollini
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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.

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Antonio Azzollini. 2011-04-26. The elliptic Kirchhoff equation in $\R^N$ perturbed by a local nonlinearity. https://arxiv.org/abs/1001.0269

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