A class of degenerate elliptic eigenvalue problems

We consider MEDIUM 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 Sheaths, Sleeves 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.