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 Flash accessories 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 Plush Toys p-Laplace operator to a much more general setting.