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

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

2008-06-07

arxiv.org/abs/0806.1266v1

Differential and integral equations 21, 7-8 (2008) 601 -- 622

Mathematics

Analysis of PDEs

Scientific paper

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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