DOI QR코드

DOI QR Code

EXISTENCE OF PERIODIC SOLUTIONS FOR A GENERAL CLASS OF p-LAPLACIAN EQUATIONS

  • Kim, Yong-In (Department of Mathematics, University of Ulsan)
  • Received : 2010.12.01
  • Accepted : 2011.02.14
  • Published : 2011.02.28

Abstract

The existence of T-periodic solutions for a general class of p-Laplacian equations is investigated. By using coincidence degree theory, some existence and uniqueness results, which generalize some earlier works on this topic, are presented.

References

  1. A. Capietto & Z. Wang: Periodic solutions of Lienard equations with asymmetric nonlinearities at resonance. J. London Math. Soc. 68 (2003), no. 2, 119-132. https://doi.org/10.1112/S0024610703004459
  2. A. Capietto, W. Dambroslo & Z. Wang: Coexistence of unbounded and periodic solutions to perturbed damped isochronous oscillators at resonance. Proc. Royal Soc. Edinburg 138A (2008), 15-32.
  3. K. Deimling: Nonlinear Functional Analysis. Springer-Verlag, Berlin, 1985.
  4. R.E. Gaines & J. Mawhin: Coincidence degree and Nonlinear differential equations, in : Lecture Notes in Mathematics. 568, Springer-Verlag, Berlin, New York, 1977.
  5. Y. Li & L. Huang: New results of periodic solutions for forced rayleigh-type equations. J. Comput. Appl. Math. 221 (2008), 98-105. https://doi.org/10.1016/j.cam.2007.10.005
  6. S. Lu & W. Ge: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear analysis: TAM 56 (2004), 501-514. https://doi.org/10.1016/j.na.2003.09.021
  7. S. Lu & Z. Gui: On the existence of periodic solutions to p-Laplacian rayleigh differential equations with a delay. J. Math. Anal. Appl. 325 (2007), 685-702. https://doi.org/10.1016/j.jmaa.2006.02.005
  8. R. Manasevich & J. Mawhin: Periodic solutions for nonlinear systems with p-Laplacian-like operators. J. Diff. Equations 145 (1998), 367-393. https://doi.org/10.1006/jdeq.1998.3425
  9. L. Wang & J. Shao: New results of periodic solutions for a kind of forced rayleigh-type equations. Nonlinear Analysis : RWA 11 (2010), 99-105. https://doi.org/10.1016/j.nonrwa.2008.10.018
  10. X. Yang: Existence of periodic solutions in nonlinear asymmetric oscillations. Bull. London Math. Soc. 37 (2005), 566-574. https://doi.org/10.1112/S0024609305004601
  11. M. Zong & H. Liang: Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments. Appl. Math. Lett. 12 (1999), 41-44. https://doi.org/10.1016/S0893-9659(98)00169-4