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

Tang, Chunlei

Nonlinear Anal., Theory Methods Appl. 32, No. 3, 299-304 (1998).

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

Keywords:

critical points theory; Palais-Smale conditions; existence; multiplicity; periodic solutions

Citations:

Zbl 0354.47025; Zbl 0676.58017

References:

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