Regular and singular solutions of a quasilinear equation with weights

Article type: Research Article

Authors: Bidaut‐Véron, Marie‐Françoise | García‐Huidobro, Marta

Affiliations: Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Faculté des Sciences, Parc Grandmont, 37200 Tours, France | Universidad Católica de Chile, Departamento de Matemáticas, Casilla 306, Correo 22, Santiago, Chile

Abstract: In this article we study the behavior near 0 of the nonnegative solutions of the equation −div(a(x)|∇u|p−2∇u)=b(x)|u|δ−1u, x∈Ω\{0}, where Ω is a domain of RN containing 0, and δ>p−1>0, a, b are nonnegative weight functions. We give a complete classification of the solutions in the radial case, and punctual estimates in the nonradial one. We also consider the Dirichlet problem in Ω.

Journal: Asymptotic Analysis, vol. 28, no. 2, pp. 115-150, 2001