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2005 Positive solution branch for elliptic problems with critical indefinite nonlinearity
Jacques Giacomoni, J. Prajapat, Mythily Ramaswamy
Differential Integral Equations 18(7): 721-764 (2005).

Abstract

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $- \Delta u =\lambda u + h (x) u^{\frac{n+2}{n-2}} $ in a smooth domain bounded (respectively, unbounded) $\Omega\subseteq\,\mathbb R^n , \ n > 4 $, for $\lambda \geq 0 $. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue $\lambda_1(\Omega)$ (respectively, the bottom of the essential spectrum).

Citation

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Jacques Giacomoni. J. Prajapat. Mythily Ramaswamy. "Positive solution branch for elliptic problems with critical indefinite nonlinearity." Differential Integral Equations 18 (7) 721 - 764, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35091
MathSciNet: MR2150656

Subjects:
Primary: 35J65
Secondary: 35B33, 35J25, 47J15, 58E05

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 7 • 2005
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