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September/October 2011 Existence and multiplicity results for equations with nearly critical growth
Francesca Gladiali, Massimo Grossi
Adv. Differential Equations 16(9/10): 801-837 (September/October 2011).

Abstract

We consider the problem \begin{equation}\nonumber \left\{ \begin{array}{ll} -\Delta u=K(x)u^{p_{\epsilon}} & \hbox{ in }\mathbb R^n\\ u>0 & \hbox{ in }\mathbb R^n \end{array}\right. \end{equation} where $p=\frac{n+2}{n-2}$, $p_{\epsilon}=p-\epsilon$, $n\geq 3$, $\epsilon>0$ and $K(x)>0$ in $\mathbb R^n$. We prove an existence and multiplicity result for single peaked solutions of our problem concentrating at a fixed critical point of $K(x)$ and some other related results.

Citation

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Francesca Gladiali. Massimo Grossi. "Existence and multiplicity results for equations with nearly critical growth." Adv. Differential Equations 16 (9/10) 801 - 837, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1232.35018
MathSciNet: MR2850754

Subjects:
Primary: 35A01, 35A02

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 9/10 • September/October 2011
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