On nonlinear eigenvalue problems
Jan H. Chabrowski · Forum Mathematicum · 1992
The aim of this paper is to establish the existence of infinite sequence of eigenvalues and eigenfunctions (μm, um) for the problem A(u) + C(u) = μB(u), where A, B and C are mappings from a real infinite dimensional Banach space X into its dual X and n is a real parameter. This is proved using minimax approach from Lusternik-Schnirelman theory of critical points. As an application we obtain the existence of infinite sequence of eigenvalues and eigenfunctions for nonlinear problems for selfadjoint elliptic operator and the p-Laplacian.