# Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains

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.
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https://hal.archives-ouvertes.fr/hal-00286004
Contributor : Ahmad El Soufi <>
Submitted on : Friday, June 6, 2008 - 5:46:35 PM
Last modification on : Wednesday, November 13, 2019 - 11:50:04 AM
Document(s) archivé(s) le : Friday, May 28, 2010 - 7:11:35 PM

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• HAL Id : hal-00286004, version 1
• ARXIV : 0806.1266

### Citation

Ahmad El Soufi, Mustapha Jazar. Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains. Differential and integral equations, Khayyam Publishing, 2008, 21 (7-8), pp.601 -- 622. ⟨hal-00286004⟩

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