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A generalized saddle point theorem. (English) Zbl 0682.34032

Summary: The well-known saddle point theorem is extended to the case of functions defined on a product space \(X\times V\), where X is a Banach space and V is a compact manifold. Under some linking conditions, the existence of at least cuplength \((V)+1\) critical points is proved. The abstract theorems are applied to the existence problems of periodic solutions of Hamiltonian systems with periodic nonlinearity and/or resonance.

MSC:

34C25 Periodic solutions to ordinary differential equations
70H05 Hamilton’s equations
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