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2008 Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains
Ahmad El Soufi, Mustapha Jazar
Differential Integral Equations 21(7-8): 601-622 (2008).

Abstract

In this paper we investigate existence and characterization of non-radial pseudo-radial (or separable) solutions of some semi-linear elliptic equations on symmetric 2-dimensional domains. The problem reduces to the phase plane analysis of a dynamical system. In particular, we give a full description of the set of pseudo-radial solutions of equations of the form $\Delta u = \pm a^2(|x|) u|u|^{q-1}$, with $q>0$, $q\neq 1$. We also study such equations over spherical or hyperbolic symmetric domains.

Citation

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Ahmad El Soufi. Mustapha Jazar. "Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains." Differential Integral Equations 21 (7-8) 601 - 622, 2008.

Information

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

zbMATH: 1224.35133
MathSciNet: MR2479683

Subjects:
Primary: 34D05, 35B99, 35C99, 35J60, 58J05

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 7-8 • 2008
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