Regular and singular solutions of a quasilinear equation with weights

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 R^N 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.