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

Ahmad El Soufi (1) , Mustapha Jazar (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Mathematics Department

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.

Mots clés: Semi-linear elliptic equations; Pseudo-radial solutions; Symmetric domains; Ordinary differential equations

Domaines: Equations aux dérivées partielles [math.AP]

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