Nonlinear eigenvalue problems for some degenerate elliptic operators on $\mathbb R^N$

Abstract

We study two nonlinear degenerate eigenvalue problems on $\mathbb R^N$. For the first problem we prove the existence of a positive eigenvalue while for the second we show the existence of a continuous family of eigenvalues. Our approach is based on standard tools in the critical point theory combined with adequate variational methods. We also apply an idea developed recently by Szulkin and Willem.