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1998 Signed solutions for a semilinear elliptic problem
Pavol Quittner
Differential Integral Equations 11(4): 551-559 (1998).

Abstract

We show existence of signed solutions with positive energy of the problem $\Delta u+u_+^p-u_-^q=0$ in $\Omega$, $u=0$ on $\partial\Omega$, where $<q<1<$, $p<(N+2)/(N-2)$ if $N>2$ and the domain $\Omega\subset\mathbb{R}^N$ is bounded and "sufficiently large.'' Our proof is based on the study of the dynamical system associated with the corresponding parabolic problem and it can be easily extended to more general problems. In particular, it does not rely on the uniqueness of the negative solution in contrast to the variational proof in [2] where the authors obtained signed solutions with negative energy.

Citation

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Pavol Quittner. "Signed solutions for a semilinear elliptic problem." Differential Integral Equations 11 (4) 551 - 559, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1131.35339
MathSciNet: MR1666269

Subjects:
Primary: 35J65

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 4 • 1998
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