Sobolev's spaces on time scales and its applications to a class of second order Hamiltonian systems on time scales

Nonlinear Analysis, Theory, Methods and Applications

Volumn 73, Issue 5, 2010, Pages 1375-1388

  Zhou, Jianwen ^a   Li, Yongkun ^a  

^a YUNNAN UNIVERSITY   (China)

Author keywords

Critical points; Hamiltonian systems; Sobolev's spaces; Time scales; Variational methods

Indexed keywords

CRITICAL POINTS; HAMILTONIAN SYSTEMS; SOBOLEV; TIME-SCALES; VARIATIONAL METHODS;

EQUATIONS OF STATE; SOBOLEV SPACES; TIME MEASUREMENT;

HAMILTONIANS;

EID: 77955327470     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2010.04.070     Document Type: Article

References (19)

1. J. Mawhin, and M. Willem Critical Point Theory and Hamiltonian Systems 1989 Springer-Verlag Berlin
2. R.P. Agarwal, V. Otero-Espinar, K. Perera, and D.R. Vivero Basic properties of Sobolev's spaces on time scales Adv. Difference Equ. 2006 2006 1 14 Article ID 38121
3. Y.K. Li, and H.T. Zhang Existence of periodic solutions for a periodic mutualism model on time scales J. Math. Anal. Appl. 343 2008 818 825
4. R.P. Agarwal, V. Otero-Espinar, K. Perera, and D.R. Vivero Multiple positive solutions of singular Dirichlet problems on time scales via variational methods Nonlinear Anal. 67 2007 368 381
5. M. Bohner, and A. Peterson Advances in Dynamic Equations on Time Scales 2003 Birkhuser Boston
6. R.P. Agarwal, M. Bohner, and W.T. Li Nonoscillation and Oscillation: Theory for Functional Differential Equations 2004 Marcel Dekker New York
7. H.T. Zhang, and Y.K. Li Existence of positive periodic solutions for functional differential equations with impulse effects on time scales Commun. Nonlinear Sci. Numer. Simul. 14 2009 19 26
8. R.P. Agarwal, and M. Bohner Basic calculus on time scales and some of its applications Results Math. 35 1999 3 22
9. M. Bohner, and A. Peterson Dynamic Equations on Time Scales: An Introduction with Applications 2001 Birkhuser Boston
10. E.R. Kaufmann, and Y.N. Raffoul Periodic solutions for a neutral nonlinear dynamical equation on a time scale J. Math. Anal. Appl. 319 2006 315 325
11. H.R. Sun, and W.T. Li Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales J. Differential Equations 240 2007 217 248
12. V. Otero-Espinar, and D.R. Vivero Existence and approximation of extremal solutions to first-order infinite systems of functional dynamic equations J. Math. Anal. Appl. 339 2008 590 597
13. Z.C. Hao, T.J. Xiao, and J. Liang Existence of positive solutions for singular boundary value problem on time scales J. Math. Anal. Appl. 325 2007 517 528
14. L.Q. Jiang, and Z. Zhou Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales Nonlinear Anal. 69 2008 1376 1388
15. R.P. Agarwal, M. Bohner, and P. Rehk Half-Linear Dynamic Equations Nonlinear Analysis and Applications to V. Lakshmikantham on his 80th Birthday vol. 1 2003 Kluwer Academic Publishers Dordrecht 1 57
16. R.P. Agarwal, M. Bohner, and P.J.Y. Wong SturmLiouville eigenvalue problems on time scales Appl. Math. Comput. 99 1999 153 166
17. 2 spaces and boundary value problems on time-scales J. Math. Anal. Appl. 328 2007 1217 1236
18. 2 spaces for boundary value problems on time-scales J. Math. Anal. Appl. 335 2007 1038 1051
19. G.Sh. Guseinov Integration on time scales J. Math. Anal. Appl. 285 2003 107 127