A dynamical system approach to the construction of singular solutions of some degenerate elliptic equations

We study the existence of singular separable solutions to the 2-dimensional quasilinear equation − •( up−2 u)+uq−1u=0 under the form u(r,θ)=r−βω(θ). We obtain the full description of the set of such solutions by combining a 2-dimensional shooting method with a phase plane analysis approach.