## Differential and Integral Equations

### 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.

#### Article information

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

Dates
First available in Project Euclid: 20 December 2012