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May/June 2012 The elliptic Kirchhoff equation in $\mathbb R^N$ perturbed by a local nonlinearity
Antonio Azzollini
Differential Integral Equations 25(5/6): 543-554 (May/June 2012).

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.

Citation

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Antonio Azzollini. "The elliptic Kirchhoff equation in $\mathbb R^N$ perturbed by a local nonlinearity." Differential Integral Equations 25 (5/6) 543 - 554, May/June 2012.

Information

Published: May/June 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1265.35069
MathSciNet: MR2951740

Subjects:
Primary: 35J20, 35J60

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.25 • No. 5/6 • May/June 2012
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