Periodic solutions for a kind of Liénard equation

Article English OPEN
Liu, Xin-Ge ; Tang, Mei-Lan ; Martin, Ralph R. (2008)
  • Publisher: Elsevier BV
  • Journal: Journal of Computational and Applied Mathematics (issn: 0377-0427, vol: 219, pp: 263-275)
  • Related identifiers: doi: 10.1016/j.cam.2007.07.024
  • Subject: Applied Mathematics | Computational Mathematics | QA75

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of T-periodic solutions for a Liénard equations with delay. An illustrative example is provided to demonstrate that the results in this paper hold under weaker conditions than existing results, and are more effective.
  • References (14)
    14 references, page 1 of 2

    [1] T.A. Burton, Stability and periodic solution of ordinary and functional differential equations, Academic Press, Orland, FL., 1985.

    [2] M.A. Del Pino, R.F. Mansevich, Multiple solutions for the p-Laplacian under global nonresonance, Proc. Amer. Math. Soc. 112 (1991) 131-138.

    [3] M.A. Del Pino, R.F. Mansevich, A. Murua, Existence and multiple of solutions with prescribed period for a second order quasi-linear ordinary differential equation, Nonlinear Anal. TMA 18 (1992) 79-92.

    [4] C. Fabry, D. Fayyad, Periodic solutions of second order differential equations with a pLaplacian and asymmetric nonlinearities, Rend. Ist. Univ. Trieste. 24 (1992) 207-227.

    [5] R.E. Gaines, J. Mawhin, Coincide degree and nonlinear differential equations, Lecture Notes in Math. Vol.568 Spring-Verlag, 1977.

    [6] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press London 1964.

    [7] X. Huang, Z. Xiang, On existence of 2π-periodic solutions for delay Duffing equation x′′ + g(t, x(t − τ (t))) = p(t), Chinese Science Bulletin 39(1994) 201-203.

    [8] B. Liu, Multiplicity results for periodic solutions of a second order quasi-linear ODE with asymmetric nonlinearities, Nonlinear Anal. TMA 33 (1998) 139-160.

    [9] B. Liu, L. Huang, Existence and uniqueness of periodic solutions for a kind of Li´enard equation with a deviating argument. Appl. Math. Lett. in press 2007.

    [10] S. Lu, W. Ge, Periodic solutions for a kind of Li´eneard equations with deviating arguments, J. Math. Anal. Appl. 249(2004) 231-243 .

  • Metrics
    No metrics available
Share - Bookmark