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

Xingyong Zhang; Xianhua Tang

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2010)

  • Volume: 54, Issue: 1
  • ISSN: 0365-1029

Abstract

top
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

top

Xingyong Zhang, and Xianhua Tang. "Periodic solutions for second-order Hamiltonian systems with a p-Laplacian." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 54.1 (2010): null. <http://eudml.org/doc/289749>.

@article{XingyongZhang2010,
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 = {Xingyong Zhang, Xianhua Tang},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Second-order Hamiltonian systems; p-Laplacian; periodic solution; Sobolev’s inequality; Wirtinger’s inequality; the least action principle},
language = {eng},
number = {1},
pages = {null},
title = {Periodic solutions for second-order Hamiltonian systems with a p-Laplacian},
url = {http://eudml.org/doc/289749},
volume = {54},
year = {2010},
}

TY - JOUR
AU - Xingyong Zhang
AU - Xianhua Tang
TI - Periodic solutions for second-order Hamiltonian systems with a p-Laplacian
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2010
VL - 54
IS - 1
SP - null
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
UR - http://eudml.org/doc/289749
ER -

References

top
  1. Berger, M.S., Schechter, M., On the solvability of semilinear gradient operator equations, Adv. Math. 25 (1977), 97-132. 
  2. Mawhin, J., Semi-coercive monotone variational problems, Acad. Roy. Belg. Bull. Cl. Sci. 73 (1987), 118-130. 
  3. Mawhin, J., Willem, M., Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989. 
  4. 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. 
  5. Rabinowitz, P. H., On subharmonic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 33 (1980), 609-633. 
  6. 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. 
  7. Tang, C. L., Periodic solutions of nonautonomous second order systems with γ -quasisubadditive potential, J. Math. Anal. Appl. 189 (1995), 671-675. 
  8. Tang, C. L., Periodic solutions of nonautonomous second order systems, J. Math. Anal. Appl. 202 (1996), 465-469. 
  9. Tang, C. L., Periodic solutions of nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), 3263-3270. 
  10. 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. 
  11. 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). 
  12. Wu, X., Saddle point characterization and multiplicity of periodic solutions of nonautonomous second order systems, Nonlinear Anal. TMA 58 (2004), 899-907. 
  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. 
  14. Zhao F., Wu, X., Periodic solutions for a class of non-autonomous second order systems, J. Math. Anal. Appl. 296 (2004), 422-434. 
  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. 
  16. Xu, B., Tang, C. L., Some existence results on periodic solutions of ordinary 
  17. p-Lapalcian systems, J. Math. Anal. Appl. 333 (2007), 1228-1236. 
  18. Tian, Y., Ge, W., Periodic solutions of non-autonoumous second-order systems with a p-Lapalcian, Nonlinear Anal. TMA 66 (2007), 192-203. 
  19. Zhang, X., Tang, X., Periodic solutions for an ordinary p-Laplacian system, Taiwanese J. Math. (in press). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.