Existence of sign changing solutions for some critical problems on $\mathbb R^N$

Norimichi Hirano; A. M. Micheletti; A. Pistoia

doi:10.3934/cpaa.2005.4.143

Article Contents

2005, Volume 4, Issue 1: 143-164. Doi: 10.3934/cpaa.2005.4.143

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Existence of sign changing solutions for some critical problems on $\mathbb R^N$

1.
Department of Mathematics, Yokohama National University, 156 Tokiwadai Hodogaya-ku - Yokohama
2.
Dipartimento di Matematica Applicata "U.Dini", Università di Pisa, Via Bonanno 25B - 56126 Pisa
3.
Dipartimento di Metodi e Modelli Matematici, Università di Roma "La Sapienza", Via Scarpa, 16 - 00166 Roma

Received: January 31, 2004

Revised: November 30, 2004

Published: February 2005

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Abstract

The main purpose of this paper is to construct families of positive and changing-sign solutions for both the slightly subcritical and slightly supercritical equations

$-\Delta u+V(x)u=N(N-2)|u|^{\frac{4}{N-2}\pm\varepsilon}u$ in $\mathbb R^N,$

which blow-up and concentrate at different points of $\mathbb R^N$ as $\varepsilon$ goes to 0, under certain conditions on the potential $V.$

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Mathematics Subject Classification: 35J60.

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Existence of sign changing solutions for some critical problems on $\mathbb R^N$

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