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2008 Existence of multiple positive solutions for a nonlinear elliptic problem with the critical exponent and a Hardy term
Norimichi Hirano, Naoki Shioji
Differential Integral Equations 21(9-10): 971-980 (2008).

Abstract

In this paper, we show that if $\mu>0$ is small enough, the problem \begin{equation*} \left\{ \begin{aligned} -\Delta u -\mu\frac{u}{|x|^2} & =|u|^{2^\ast-2}u & & \text{in $\Omega$,}\\ u & =0 & & \text{on $\partial\Omega$} \end{aligned} \right. \end{equation*} has at least cat $\Omega -1$ positive solutions, where $\Omega$ is a noncontractible, bounded domain in $\mathbb R^N (N\geq 4)$ such that its boundary is smooth and $0 \in \Omega$.

Citation

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Norimichi Hirano. Naoki Shioji. "Existence of multiple positive solutions for a nonlinear elliptic problem with the critical exponent and a Hardy term." Differential Integral Equations 21 (9-10) 971 - 980, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35134
MathSciNet: MR2483344

Subjects:
Primary: 35J60
Secondary: 35B33, 47J30

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 9-10 • 2008
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