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On the existence of eigenvalues for some nonlinear elliptic and hyperbolic problems

Synopsis In this paper some eigenvalue problems for elliptic as well as hyperbolic equations are solved. The main tool used is an abstract critical point theorem on an unbounded manifold of the form {u | (Lu, u) = constant} (where L is a nonpositive selfadjoint operator), which makes use of a linking type argument on a manifold.