A bifurcation phenomenon for the critical Laplace and p-Laplace equation in the ball

Abstract

We consider radial positive solutions for a class of quasilinear differential equations ruled by the p-Laplace differential operator with a critical weighted nonlinearity. We show that the problem undergoes a bifurcation phenomenon. We provide a new multiplicity result, even in the classical Laplace case. The proofs use the Fowler transformation and dynamical systems tools.