Singular solutions to a quasilinear ODE

In this paper, we prove the existence of infinitely many radial solutions having a singular behaviour at the origin for a superlinear problem of the form −Δpu=|u|δ−1u in B(0,1)∖{0}⊂RN,\, u=0 for |x|=1, where N>p>1 and δ>p−1. Solutions are characterized by their nodal properties. The case δ+1<NpN−p is treated. The study of the singularity is based on some energy considerations and takes into account the classification of the behaviour of the possible solutions available in the literature. By following a shooting approach, we are able to deduce the main multiplicity result from some estimates on the rotation numbers associated to the solutions.