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Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems. (English) Zbl 1118.34038

Periodic and subharmonic solutions of a class of subquadratic nonautonomous second order Hamiltonian systems are considered. Such problems were investigated by P. Rabinowitz in 1980. In the present paper employing some new solvability conditions based on minimax methods in critical point theory, a generalization of the results of Rabinowitz and other related to this topic more recent results (by another authors) is obtained. Two theorems concerning these solutions are formulated and proved.

MSC:

34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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