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2004 Existence and multiplicity for perturbations of an equation involving a Hardy inequality and the critical Sobolev exponent in the whole of $\Bbb R^N$
B. Abdellaoui, V. Felli, I. Peral
Adv. Differential Equations 9(5-6): 481-508 (2004).

Abstract

In order to obtain solutions to the problem $$ \left\{ \begin{array}{c} -\Delta u=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1},\,\,x\in {{{\mathbb R}}^N}, \\ u>0 \hbox{ in }{{{\mathbb R}}^N}, \mbox{ and }u\in {{\mathcal D}^{1,2}}({{{\mathbb R}}^N}), \end{array} \right. $$ $h$ and $k$ must be chosen taking into account not only the size of some norm but the shape. Moreover, if $h(x)\equiv 0$, to reach a multiplicity of solutions, some hypotheses about the local behavior of $k$ close to the points of maximum are needed.

Citation

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B. Abdellaoui. V. Felli. I. Peral. "Existence and multiplicity for perturbations of an equation involving a Hardy inequality and the critical Sobolev exponent in the whole of $\Bbb R^N$." Adv. Differential Equations 9 (5-6) 481 - 508, 2004.

Information

Published: 2004
First available in Project Euclid: 18 December 2012

zbMATH: 1220.35041
MathSciNet: MR2099969

Subjects:
Primary: 35J60
Secondary: 35B33, 35D05, 35J20, 46E35, 47J30

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.9 • No. 5-6 • 2004
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