A generalized saddle point theorem. (English) Zbl 0682.34032

Liu, J. Q.

J. Differ. Equations 82, No. 2, 372-385 (1989).

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

Keywords:

saddle point; Hamiltonian systems; resonance

References:

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