Pseudo-radial solutions of semi-linear elliptic equations on symmetric domains. (English) Zbl 1224.35133

El Soufi, Ahmad; Jazar, Mustapha

Differ. Integral Equ. 21, No. 7-8, 601-622 (2008).

Summary: 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 to 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.

MSC:

35J61	Semilinear elliptic equations
35R01	PDEs on manifolds
34D05	Asymptotic properties of solutions to ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

semi-linear elliptic equation; dynamical system; pseudo-radial solution