Infinitely many solutions and Morse index for non-autonomous elliptic problems

Abstract

This paper deals with changes of variables, and the exact bifurcation diagrams for a class of self-similar equations. Our first result is a change of variables which transforms radial $ k $-Hessian equations into radial $ p $-Laplace equations. Then, in another direction, we generalize the classical results of D.D. Joseph and T.S. Lundgren [10] by using the method we developed in [13] and [14]. We provide a considerably simpler approach, which yields additional information on the Morse index of solutions.