Periodic solutions for second-order Hamiltonian systems with a p-Laplacian

Xingyong Zhang, Xianhua Tang

Abstract


In this paper, by using the least action principle, Sobolev’s inequality and Wirtinger’s inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.

Keywords


Second-order Hamiltonian systems; p-Laplacian; periodic solution; Sobolev’s inequality; Wirtinger’s inequality; the least action principle

Full Text:

PDF

References


Berger, M.S., Schechter, M., On the solvability of semilinear gradient operator equations, Adv. Math. 25 (1977), 97-132.

Mawhin, J., Semi-coercive monotone variational problems, Acad. Roy. Belg. Bull. Cl. Sci. 73 (1987), 118-130.

Mawhin, J., Willem, M., Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989.

Mawhin, J., Willem, M., Critical points of convex perturbations of some indefinite quadratic forms and semilinear boundary value problems at resonance, Ann. Inst. H. Poincare Anal. Non Lin´eaire 3 (1986), 431-453.

Rabinowitz, P. H., On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 33 (1980), 609-633.

Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, in: CBMS Regional Conf. Ser. in Math., Vol. 65, American Mathematical Society, Providence, RI, 1986.

Tang, C. L., Periodic solutions of nonautonomous second order systems with (gamma)-quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), 671-675.

Tang, C. L., Periodic solutions of nonautonomous second order systems, J. Math. Anal. Appl. 202 (1996), 465-469.

Tang, C. L., Periodic solutions of nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), 3263-3270.

Tang, C. L.,Wu, X. P., Periodic solutions for second order systems with not uniformly coercive potential, J. Math. Anal. Appl. 259 (2001), 386-397.

Willem, M., Oscillations forcees de systemes hamiltoniens, Publ. Math. Fac. Sci. Besancon, Anal. Non Lineaire Annee 1980-1981, Expose No. 4, 16 p. (1981) (French).

Wu, X., Saddle point characterization and multiplicity of periodic solutions of nonautonomous second order systems, Nonlinear Anal. TMA 58 (2004), 899-907.

Wu, X. P., Tang, C. L., Periodic solutions of a class of nonautonomous second order systems, J. Math. Anal. Appl. 236 (1999), 227-235.

Zhao F., Wu, X., Periodic solutions for a class of non-autonomous second order systems, J. Math. Anal. Appl. 296 (2004), 422-434.

Zhao F., Wu, X., Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity, Nonlinear Anal. 60 (2005), 325-335.

Xu, B., Tang, C. L., Some existence results on periodic solutions of ordinary

p-Lapalcian systems, J. Math. Anal. Appl. 333 (2007), 1228-1236.

Tian, Y., Ge, W., Periodic solutions of non-autonoumous second-order systems with a p-Lapalcian, Nonlinear Anal. TMA 66 (2007), 192-203.

Zhang, X., Tang, X., Periodic solutions for an ordinary p-Laplacian system, Taiwanese J. Math. (in press).




DOI: http://dx.doi.org/10.2478/v10062-010-0008-8
Date of publication: 2016-07-29 22:06:17
Date of submission: 2016-07-29 21:55:47


Statistics


Total abstract view - 761
Downloads (from 2020-06-17) - PDF - 462

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 Xingyong Zhang, Xianhua Tang