×

Existence and multiplicity of periodic solutions for nonautonomous second order systems. (English) Zbl 0949.34032

This paper is concerned with existence and multiplicity of periodic solutions to second-order systems \[ \ddot u=\nabla F(t,u(t)). \] By classical theorems of critical points theory, the author generalizes some previous results obtained by M. S. Berger and M. Schechter [Adv. Math. 25, 97-132 (1977; Zbl 0354.47025)], and J. Mawhin and M. Willem [Critical point theory and Hamiltonian systems. New York etc.: Springer-Verlag (1989; Zbl 0676.58017)].
Reviewer: Bin Liu (Beijing)

MSC:

34C25 Periodic solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Berger, M.S.; Schechter, M., On the solvability of semilinear gradient operator equations, Advances in math., 25, 97-132, (1977) · Zbl 0354.47025
[2] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian systems, (1989), Springer-Verlag New York · Zbl 0676.58017
[3] Tang, C.L., Periodic solutions of nonautonomous second order systems, J. math. anal. appl., 202, 465-469, (1996) · Zbl 0857.34044
[4] Brezis, H.; Nirenberg, L., Remarks on finding critical points, Comm. pure appl. math., 44, 939-963, (1991) · Zbl 0751.58006
[5] Long, Y.M., Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials, Nonlinear analysis, 24, 12, 1665-1671, (1995) · Zbl 0824.34042
[6] Tang, C.L., Periodic solutions of nonautonomous second order systems with γ-quasisubadditive potential, J. math. anal. appl., 189, 3, 671-675, (1995) · Zbl 0824.34043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.