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

Xianhua Tang; Xingyong Zhang

Annales UMCS, Mathematica (2010)

  • Volume: 64, Issue: 1, page 93-113
  • ISSN: 2083-7402

Abstract

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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.

How to cite

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Xianhua Tang, and Xingyong Zhang. " Periodic solutions for second-order Hamiltonian systems with a p -Laplacian ." Annales UMCS, Mathematica 64.1 (2010): 93-113. <http://eudml.org/doc/267551>.

@article{XianhuaTang2010,
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.},
author = {Xianhua Tang, Xingyong Zhang},
journal = {Annales UMCS, Mathematica},
keywords = {Second-order Hamiltonian systems; p-Laplacian; periodic solution; Sobolev's inequality; Wirtinger's inequality; the least action principle; second-order Hamiltonian systems; -Laplacian; least action principle},
language = {eng},
number = {1},
pages = {93-113},
title = { Periodic solutions for second-order Hamiltonian systems with a p -Laplacian },
url = {http://eudml.org/doc/267551},
volume = {64},
year = {2010},
}

TY - JOUR
AU - Xianhua Tang
AU - Xingyong Zhang
TI - Periodic solutions for second-order Hamiltonian systems with a p -Laplacian
JO - Annales UMCS, Mathematica
PY - 2010
VL - 64
IS - 1
SP - 93
EP - 113
AB - 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.
LA - eng
KW - Second-order Hamiltonian systems; p-Laplacian; periodic solution; Sobolev's inequality; Wirtinger's inequality; the least action principle; second-order Hamiltonian systems; -Laplacian; least action principle
UR - http://eudml.org/doc/267551
ER -

References

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  11. Willem, M., Oscillations forcees de systèmes hamiltoniens, Publ. Math. Fac. Sci. Besancon, Anal. Non Lineaire Annee 1980-1981, Expose No. 4, 16 p. (1981) (French). Zbl0482.70020
  12. Wu, X., Saddle point characterization and multiplicity of periodic solutions of nonautonomous second order systems, Nonlinear Anal. TMA 58 (2004), 899-907. Zbl1058.34053
  13. Wu, X. P., Tang, C. L., Periodic solutions of a class of nonautonomous second order systems, J. Math. Anal. Appl. 236 (1999), 227-235. Zbl0971.34027
  14. Zhao F., Wu, X., Periodic solutions for a class of non-autonomous second order systems, J. Math. Anal. Appl. 296 (2004), 422-434. Zbl1050.34062
  15. 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. Zbl1087.34022
  16. Xu, B., Tang, C. L., Some existence results on periodic solutions of ordinary p-Lapalcian systems, J. Math. Anal. Appl. 333 (2007), 1228-1236. Zbl1154.34331
  17. Tian, Y., Ge, W., Periodic solutions of non-autonoumous second-order systems with a p-Lapalcian, Nonlinear Anal. TMA 66 (2007), 192-203. 
  18. Zhang, X., Tang, X., Periodic solutions for an ordinary p-Laplacian system, Taiwanese J. Math. (in press). Zbl1237.34088

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