Separable solutions of some quasilinear equations with source reaction

We study the existence of singular solutions to the equation −div(Dup−2Du)=uq−1u under the form u(r,θ)=r−βω(θ), r>0, θ SN−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.