Existence of infinitely many periodic solutions for ordinary \(p\)-Laplacian systems. (English) Zbl 1153.37009

Summary: We study the existence and multiplicity of non-trivial periodic solutions of ordinary \(p\)-Laplacian systems by using the minimax technique in critical point theory. We also give an example to illustrate that the obtained results are new even in the case \(p=2\).


37C10 Dynamics induced by flows and semiflows
34C25 Periodic solutions to ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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[1] Bartolo, P.; Benci, V.; Fortunato, D., Abstract critical point theorems and applications to some problems with strong resonance at infinity, Nonlinear anal. (TMA), 7, 241-273, (1983) · Zbl 0522.58012
[2] Cerami, G., An existence criterion for the critical points on unbounded manifolds, Istit. lombardo accad. sci. lett. rend. A, 112, 332-336, (1978), (in Italian) · Zbl 0436.58006
[3] Fei, G., On periodic solutions of superquadratic Hamiltonian systems, Electron. J. differential equations, 08, 1-12, (2002) · Zbl 0999.37039
[4] Jiang, Q.; Tang, C.-L., Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems, J. math. anal. appl., 328, 380-389, (2007) · Zbl 1118.34038
[5] Mawhin, J.; Willem, M., Critical point theory and Hamiltonian system, Appl. math. sci., vol. 74, (1989), Springer-Verlag New York
[6] D. Pasca, C.-L. Tang, Subharmonic solutions for nonautonomous sublinear second-order differential inclusions systems with p-Laplacian, Nonlinear Anal. (2008), in press · Zbl 1160.34008
[7] Rabinowitz, P., Minimax methods in critical point theory with applications to differential equations, CBMS reg. conf. ser. math., vol. 65, (1986), Amer. Math. Soc. Providence, RI
[8] Rabinowitz, P., Periodic solutions of Hamiltonian systems, Comm. pure appl. math., 31, 157-184, (1978) · Zbl 0358.70014
[9] Rabinowitz, P., On subharmonic solutions of Hamiltonian systems, Comm. pure appl. math., 33, 609-633, (1980) · Zbl 0425.34024
[10] Tang, C.-L.; Wu, X.-P., Periodic solutions of second order systems with not uniformly coercive potential, J. math. anal. appl., 259, 386-397, (2001) · Zbl 0999.34039
[11] Tang, C.-L.; Wu, X.-P., Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems, J. math. anal. appl., 275, 870-882, (2002) · Zbl 1043.34045
[12] Tang, C.-L.; Wu, X.-P., Notes on periodic solutions of subquadratic second order systems, J. math. anal. appl., 285, 8-16, (2003) · Zbl 1054.34075
[13] Tao, Z.-L.; Tang, C.-L., Periodic solutions of second-order Hamiltonian systems, J. math. anal. appl., 293, 435-445, (2004) · Zbl 1042.37047
[14] Xu, B.; Tang, C.-L., Some existence results on periodic solutions of ordinary p-Laplacian systems, J. math. anal. appl., 333, 1228-1236, (2007) · Zbl 1154.34331
[15] Zou, W., Multiple solutions for second-order Hamiltonian systems via computation of the critical groups, Nonlinear anal., 44, 975-989, (2001) · Zbl 0997.37039
[16] Zou, W.; Li, S., Infinitely many solutions for Hamiltonian systems, J. differential equations, 186, 141-164, (2002)
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