# SOME EXISTENCE RESULTS ON PERIODIC SOLUTIONS OF ORDINARY (q, p)-LAPLACIAN SYSTEMS

• Pasca, Daniel (Department of Mathematics and Informatics, University of Oradea) ;
• Tang, Chun-Lei (School of Mathematics and Statistics, Southwest University)
• Accepted : 2010.06.10
• Published : 2011.01.30

#### Abstract

Some existence theorems are obtained for periodic solutions of nonautonomous second-order differential systems with (q, p)-Laplacian by the minimax methods in critical point theory.

#### Acknowledgement

Supported by : National Natural Science Foundation of China

#### References

1. E. Hewitt and K. Stromberg - Real and Abstract Analysis, Springer, New York, 1965.
2. P. Jebelean and R. Precup -Solvability of p, q-Laplacian systems with potential boundary conditions, Appl.Anal. (2009) (in press).
3. J. Mawhin and M. Willem - Critical Point Theory and Hamiltonian Systems, Springer-Verlag, Berlin/New York, 1989.
4. D. Pasca - Periodic Solutions for Second Order Differential Inclusions, Communications on Applied Nonlinear Analysis, 6 4 (1999) 91-98.
5. D. Pasca - Periodic Solutions for Second Order Differential Inclusions with Sublinear Nonlinearity, PanAmerican Mathematical Journal, vol. 10, nr. 4 (2000) 35-45.
6. D. Pasca - Periodic Solutions of a Class of Non-autonomous Second Order Differential Inclusions Systems, Abstract and Applied Analysis, vol. 6, nr. 3 (2001) 151-161. https://doi.org/10.1155/S1085337501000525
7. D. Pasca - Periodic solutions of second-order differential inclusions systems with p-Laplacian, J. Math. Anal. Appl., vol. 325, nr. 1 (2007) 90-100. https://doi.org/10.1016/j.jmaa.2006.01.061
8. D. Pasca - Periodic solutions of a class of nonautonomous second order differential systems with (q, p)-Laplacian, Bulletin of the Belgian Mathematical Society - Simon Stevin (2009) (in press).
9. D. Pasca and C.-L. Tang - Subharmonic solutions for nonautonomous sublinear second order differential inclusions systems with p-Laplacian, Nonlinear Analysis: Theory, Methods & Applications, 69 (2008) 1083-1090. https://doi.org/10.1016/j.na.2007.06.019
10. D. Pasca and C.-L. Tang - Some existence results on periodic solutions of nonautonomous second order differential systems with (q, p)-Laplacian, Appl.Math.Letters, 23 (2010) 246-251. https://doi.org/10.1016/j.aml.2009.10.005
11. P. H. Rabinowitz - Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. in Math. No. 65, AMS, Providence, RI, 1986.
12. C.-L. Tang - Periodic Solutions of Non-autonomous Second-Order Systems with $\gamma$-Quasisubadditive Potential, J. Math. Anal. Appl., 189 (1995), 671-675. https://doi.org/10.1006/jmaa.1995.1044
13. C.-L. Tang - Periodic Solutions of Non-autonomous Second Order Systems, J. Math. Anal. Appl., 202 (1996), 465-{469. https://doi.org/10.1006/jmaa.1996.0327
14. C.-L. Tang - Periodic Solutions for Nonautonomous Second Order Systems with Sublinear Nonlinearity, Proc. AMS, 126 (1998), 3263-3270. https://doi.org/10.1090/S0002-9939-98-04706-6
15. C.-L. Tang - Existence and Multiplicity of Periodic Solutions of Nonautonomous Second Order Systems, Nonlinear Analysis, 32 (1998), 299-304. https://doi.org/10.1016/S0362-546X(97)00493-8
16. Y. Tian and W. Ge - Periodic solutions of non-autonomous second-order systems with a p-Laplacian, Nonlinear Analysis 66 (2007), 192-203. https://doi.org/10.1016/j.na.2005.11.020
17. J. Ma and C.-L. Tang - Periodic Solutions for Some Nonautonomous Second-Order Systems, J. Math. Anal. Appl. 275 (2002), 482-494. https://doi.org/10.1016/S0022-247X(02)00636-4
18. X.-P. Wu - Periodic Solutions for Nonautonomous Second-Order Systems with Bounded Nonlinearity, J. Math. Anal. Appl. 230 (1999), 135-141. https://doi.org/10.1006/jmaa.1998.6181
19. X.-P.Wu and C.-L. Tang - Periodic Solutions of a Class of Non-autonomous Second-Order Systems, J. Math. Anal. Appl. 236 (1999), 227-235. https://doi.org/10.1006/jmaa.1999.6408
20. X.-P. Wu and C.-L. Tang - Periodic Solutions of Nonautonomous Second-Order Hamiltonian Systems with Even-Typed Potentials, Nonlinear Analysis 55 (2003), 759-769. https://doi.org/10.1016/j.na.2003.08.009
21. F. Zhao and X. Wu - Saddle Point Reduction Method for Some Non-autonomous Second Order Systems, J. Math. Anal. Appl. 291 (2004), 653-665. https://doi.org/10.1016/j.jmaa.2003.11.019
22. C.-L. Tang and X.-P. Wu - Periodic Solutions for Second Order Systems with Not Uni- formly Coercive Potential, J. Math. Anal. Appl. 259 (2001), 386-397. https://doi.org/10.1006/jmaa.2000.7401
23. C.-L. Tang and X.-P. Wu - Notes on Periodic Solutions of Subquadratic Second Order Systems, J. Math. Anal. Appl. 285 (2003), 8-16. https://doi.org/10.1016/S0022-247X(02)00417-1
24. C.-L. Tang and X.-P. Wu - Subharmonic Solutions for Nonautonomous Second Order Hamiltonian Systems, J. Math. Anal. Appl. 304 (2005), 383-393. https://doi.org/10.1016/j.jmaa.2004.09.032
25. B. Xu and C.-L. Tang - Some existence results on periodic solutions of ordinary p-Laplacian systems, J.Math.Anal.Appl. 333 (2007) 1228-1236. https://doi.org/10.1016/j.jmaa.2006.11.051