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

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March 2005, 4(1): 143-164. doi: 10.3934/cpaa.2005.4.143

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

Norimichi Hirano ^1, , A. M. Micheletti ^2, and A. Pistoia ^3,

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

Received February 2004 Revised December 2004 Published December 2004

Abstract
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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 $V.$

Keywords: blowing-up solution, sign changing solutions., critical Sobolev exponent.

Mathematics Subject Classification: 35J6.

Citation: Norimichi Hirano, A. M. Micheletti, A. Pistoia. Existence of sign changing solutions for some critical problems on $\mathbb R^N$. Communications on Pure & Applied Analysis, 2005, 4 (1) : 143-164. doi: 10.3934/cpaa.2005.4.143

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