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Periodic solutions for second-order Hamiltonian systems with a \(p\)-Laplacian. (English) Zbl 1219.34057

The authors considered two second-order Hamiltonian systems with a \(p\)-Laplacian. Using the improved Sobolev inequality and Wirtinger’s inequality, and the least action principle, they obtain some existence conditions for periodic solutions of these two systems.

MSC:

34C25 Periodic solutions to ordinary differential equations
70H05 Hamilton’s equations
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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