Location and critical groups of critical points in Banach spaces with an application to nonlinear eigenvalue problems

Abstract

We develop critical-point theory in Banach spaces in order to find critical points inside or outside of given convex subsets of the space. In addition to localizing critical points we also obtain results on their critical groups. The abstract theory can be applied to $p$-Laplacian equations in order to prove the existence of multiple sign-changing solutions.