A class of degenerate elliptic eigenvalue problems

A class of degenerate elliptic eigenvalue problems

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We consider a general class mr robot sticker 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 bernhardt arctic dining table of the p-Laplace operator to a much more general setting.