ISOLATED CONNECTED EIGENVALUES IN NONLINEAR SPECTRAL THEORY

Abstract

The existence of eigenvalues for nonlinear homogeneous operators is discussed, considering perturbations of linear operators having a simple isolated eigenvalue. It is shown in particular that the nonlinear eigenvalues themselves are isolated. The proof is based on the Lyapounov-Schmidt reduction. The result is applied to a class of semilinear elliptic operators in bounded domains of R^N.