×

Periodic solutions for some nonautonomous second-order systems. (English) Zbl 1024.34036

Some existence theorems are obtained for periodic solutions to second-order systems using the least action principle and minimax methods. The second-order system considered is of the form \[ \ddot u=\nabla F(t, u(t)),\quad u(0)- u(T)= 0,\qquad\dot u(0)-\dot u(T)= 0, \] where \(T> 0\) and \(F: [0,T]\times \mathbb{R}^N\to\mathbb{R}\) and \(F\) satisfies specified conditions.
Reviewer: P.Smith (Keele)

MSC:

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

References:

[1] Tang, C.L., Periodic solutions for nonautonomous second systems with sublinear nonlinearity, Proc. amer. math. soc., 126, 3263-3270, (1998) · Zbl 0902.34036
[2] Ahmad, S.; Lazer, A.C., Critical point theory and a theorem of amral and pea, Boll. un. mat. ital. B, 3, 583-598, (1984) · Zbl 0603.34036
[3] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian systems, (1989), Springer-Verlag New York · Zbl 0676.58017
[4] Tang, C.L., Periodic solutions of nonautonomous second order systems with γ-quasisubadditive potential, J. math. anal. appl., 189, 671-675, (1995) · Zbl 0824.34043
[5] Tang, C.L., Existence and multiplicity of periodic solutions for nonautonomous second order systems, Nonlinear anal., 32, 299-304, (1998) · Zbl 0949.34032
[6] Long, Y.M., Nonlinear oscillations for classical Hamiltonian systems with bi-even subquadratic potentials, Nonlinear anal., 24, 1665-1671, (1995) · Zbl 0824.34042
[7] Mawhin, J., Semi-coercive monotone variational problems, Acad. roy. belg. bull. cl. sci., 73, 118-130, (1987) · Zbl 0647.49007
[8] Berger, M.S.; Schechter, M., On the solvability of semilinear gradient operator equations, Adv. math., 25, 97-132, (1977) · Zbl 0354.47025
[9] Tang, C.L., Periodic solutions of nonautonomous second order systems, J. math. anal. appl., 202, 465-469, (1996) · Zbl 0857.34044
[10] Willem, M., Oscillations forcées de systèmes hamiltoniens, () · Zbl 0482.70020
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.