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Periodic solutions to differential equations with a generalized p-Laplacian

Abstract Related Papers Cited by
  • The existence of a periodic solution to nonlinear ODEs with $\varphi$-Laplacian is proved under conditions on functions given in the equation (not on the unknown solutions). The results are applied to a relativistic pendulum equation in a general form.
    Mathematics Subject Classification: 34C25, 47H11.

    Citation:

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  • [1]

    C. Bereanu, P. Jebelean and J. Mawhin, Periodic solutions of pendulum-like perturbations of singular and bounded $\phi$-Laplacians, J. Dynam. Differential Equations, 22 (2010), 463-471.doi: 10.1007/s10884-010-9172-3.

    [2]

    C. Bereanu and J. Mawhin, Existence and multiplicity results for some nonlinear problems with singular $\phi$-Laplacian, J. Differential Equations, 243 (2007), 536-557.doi: 10.1016/j.jde.2007.05.014.

    [3]

    C. Bereanu and P. J. Torres, Existence of at least two periodic solutions of the forced relativistic pendulum, Proc. Amer. Math. Soc., 140 (2012), 2713-2719.doi: 10.1090/S0002-9939-2011-11101-8.

    [4]

    H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum, Differential Integral Equations, 23 (2010), 801-810.

    [5]

    J. A. Cid and P. J. Torres, On the existence and stability of periodic solutions for pendulum-like equations with friction and $\phi$-Laplacian, Discrete Contin. Dyn. Syst., 33 (2013), 141-152.doi: 10.3934/dcds.2013.33.141.

    [6]

    W. Ge and J. Ren, An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacian, Nonl. Anal. TMA, 58 (2004), 477-488.doi: 10.1016/j.na.2004.01.007.

    [7]

    S. Ma and Y. Zhang, Existence of infinitely many periodic solutions for ordinary p-Laplacian systems, J. Math. Anal. Appl., 351 (2009), 469-479.doi: 10.1016/j.jmaa.2008.10.027.

    [8]

    R. Manásevich and J. Mawhin, Periodic solutions for nonlinear systems with p-Laplacian-like operators, J. Differential Equations, 145 (1998), 367-393.doi: 10.1006/jdeq.1998.3425.

    [9]

    R. Manásevich and J. Mawhin, Boundary value problems for nonlinear perturbations of vector p-Laplacian-like operators, J. Korean Math. Soc., 37 (2000), 665-685.

    [10]

    J. Mawhin, Periodic solutions of the forced pendulum: Classical vs relativistic, Le Mathematiche, 65 (2010), 97-107.

    [11]

    Xiang Lv, Shiping Lu and Ping Yan, Periodic solutions of non-autonomous ordinary p-Laplacian systems, J. Appl. Math. Comput., 35 (2011), 11-18.doi: 10.1007/s12190-009-0336-4.

    [12]

    P. J. Torres, Nondegeneracy of the periodically forced Liénard differential equation with $\phi$-Laplacian, Commun. Contemp. Mathematics, 13 (2011), 283-292.doi: 10.1142/S0219199711004208.

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