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Non-autonomous second order Hamiltonian systems. (English) Zbl 1331.37085

Summary: We study the existence of periodic solutions for a second order non-autonomous dynamical system containing variable kinetic energy terms. Our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other. We study sublinear problems and the existence of non-constant solutions.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
35Q55 NLS equations (nonlinear Schrödinger equations)
47J30 Variational methods involving nonlinear operators
49J40 Variational inequalities
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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