Differential and Integral Equations

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

Ahmad El Soufi and Mustapha Jazar

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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.

Article information

Source
Differential Integral Equations, Volume 21, Number 7-8 (2008), 601-622.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038614

Mathematical Reviews number (MathSciNet)
MR2479683

Zentralblatt MATH identifier
1224.35133

Subjects
Primary: 35J60: Nonlinear elliptic equations 58J05: Elliptic equations on manifolds, general theory [See also 35-XX] 34D05: Asymptotic properties 35B99: None of the above, but in this section 35C99: None of the above, but in this section

Citation

El Soufi, Ahmad; Jazar, Mustapha. Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains. Differential Integral Equations 21 (2008), no. 7-8, 601--622. https://projecteuclid.org/euclid.die/1356038614


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