Separable solutions of some quasilinear equations with source reaction

Marie-Françoise Bidaut-Veron (1) , Mustapha Jazar (2) , Laurent Veron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 Department of Mathematics [Beirut]

We study the existence of singular solutions to the equation $-div (|Du|^{p-2}D u)=| u|^{q-1}u$ under the form $u(r,\theta)=r^{-\beta}\omega(\theta)$, $r>0,\theta\in S^{N-1}$. We prove the existence of an exponent $q$ below which no positive solutions can exist. If the dimension is $2$ we use a dynamical system approach to construct solutions.

Mots clés: $p$-Laplacian; Singularities; Phase-plane analysis; Poincaré map; Painlevé integral

Domaines: Equations aux dérivées partielles [math.AP]

Marie-Françoise Bidaut-Veron, Mustapha Jazar, Laurent Veron. Separable solutions of some quasilinear equations with source reaction. Journal of Differential Equations, 2008, 244, pp.274-308. ⟨hal-00282539⟩