A class of degenerate elliptic eigenvalue problems

Abstract

We consider a general class of eigenvalue problems where the leading elliptic term corresponds to a convex homogeneous energy function that is not necessarily differentiable. We derive a strong maximum principle and show uniqueness of the first eigenfunction. Moreover we prove the existence of a sequence of eigensolutions by using a critical point theory in metric spaces. Our results extend the eigenvalue problem of the p-Laplace operator to a much more general setting.

Keywords

• nonlinear eigenvalue problems
• quasilinear elliptic equations
• critical point theory
• convex analysis
• nonsmooth analysis