Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

PERIODIC SOLUTIONS FOR DUFFING TYPE p-LAPLACIAN EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

  • Jiang, Ani (College of Mathematics and Computer Science, Hunan University of Arts and Science)
  • Received : 2012.01.20
  • Accepted : 2012.05.22
  • Published : 2013.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider the Duffing type p-Laplacian equation with multiple deviating arguments of the form $$({\varphi}_p(x^{\prime}(t)))^{\prime}+Cx^{\prime}(t)+go(t,x(t))+\sum_{k=1}^ngk(t,x(t-{\tau}_k(t)))=e(t)$$. By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation. Moreover, an example is given to illustrate the effectiveness of our results.

Keywords

References

  1. F. Gao, S. Lu, W. Zhang, Existence and uniqueness of periodic solutions for a p-Laplacian Duffing equation with a deviating argument, Nonlinear Anal. 70 (2009), 3567-3574. https://doi.org/10.1016/j.na.2008.07.014
  2. 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
  3. B. Liu, Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with two deviating arguments, Comput. & Math. Appl. 55(9) (2008), 2108-2117. https://doi.org/10.1016/j.camwa.2007.08.042
  4. S. Lu, W. Ge, Periodic solutions for a kind of second order differential equation with multiple deviating arguments, Appl. Math. Computat. 146(1) (2004), 195-209.
  5. R. Manasevich, J. Mawhin, Periodic solutions for nonlinear systems with p-Lplacian-like operators, J. Differential Equations 145 (1998), 367-393. https://doi.org/10.1006/jdeq.1998.3425
  6. A. Sirma, C. Tunc S. Ozlem, Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with finitely many deviating arguments, Nonlinear Anal. 73(2) (2010), 358-366. https://doi.org/10.1016/j.na.2010.03.024
  7. M. L. Tang, X. G. Liu , Periodic solutions for a kind of Duffing type p-Laplacian equation, Nonlinear Anal. 71 (2009), 1870-1875. https://doi.org/10.1016/j.na.2009.01.022
  8. Y. Tang, Y. Li, New results of periodic solutions for a kind of Duffing type p-Laplacian equation, J. Math. Anal. Appl. 340(2) (2008), 1380-1384. https://doi.org/10.1016/j.jmaa.2007.10.007
  9. Y. Wang , Novel existence and uniqueness criteria for periodic solutions of a Duffing type p-Laplacian equation, Appl. Math. Lett. 23 (2010), 436-439. https://doi.org/10.1016/j.aml.2009.11.013
  10. Z. Wang, L. Qian, S. Lu, J. Cao, The existence and uniqueness of periodic solutions for a kind of Duffing-type equation with two deviating arguments, Nonlinear Anal. 73 (2010), 3034-3043. https://doi.org/10.1016/j.na.2010.06.071
  11. H. Zhang, J. Meng, Periodic Solutions for Duffing Type p-Laplacian Equation with Multiple Constant Delays, Abstract and Applied Analysis Volume 2012, Article ID 760918, 9 pages doi:10.1155/2012/760918.