Advanced Search
Article Contents
Article Contents

Three nonzero periodic solutions for a differential inclusion

Abstract Related Papers Cited by
  • We prove the existence of three non-zero periodic solutions for an ordinary differential inclusion. Our approach is variational and based on a multiplicity theorem for the critical points of a nonsmooth functional, which extends a recent result of Ricceri.
    Mathematics Subject Classification: Primary: 34A60; Secondary: 34C25.


    \begin{equation} \\ \end{equation}
  • [1]

    G. Bonanno, A minimax inequality and its applications to ordinary differential equations, J. Math. Anal. Appl., 270 (2002), 210-229.doi: 10.1016/S0022-247X(02)00068-9.


    A. Boucherif and S. M. Bouguima, Periodic solutions of second [order] ordinary differential equations with a discontinuous nonlinearity, in "Nonlinear Partial Differential Equations" (Fès, 1994), Pitman Res. Notes Math. Ser., 343, Longman, Harlow, (1996), 54-60.


    K. C. Chang, Variational methods for nondifferentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102-129.doi: 10.1016/0022-247X(81)90095-0.


    L. H. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions $y''\in F(t,y,y')$, Ann. Polon. Math., 54 (1991), 195-226.


    M. Frigon and A. Granas, Problèmes aux limites pour des inclusions différentielles de type semi-continues inférieurement, Riv. Mat. Univ. Parma (4), 17 (1991), 87-97.


    A. Iannizzotto, Three critical points for perturbed nonsmooth functionals and applications, Nonlinear Anal., 72 (2010), 1319-1338.doi: 10.1016/j.na.2009.08.001.


    D. Kandilakis, N. C. Kourogenis and N. S. Papageorgiou, Two nontrivial critical points for nonsmooth functionals via local linking and applications, J. Global Optim., 34 (2006), 219-244.doi: 10.1007/s10898-005-3884-7.


    M. Krastanov, N. Ribarska and T. Tsachev, A note on: "On a critical point theory for multivalued functionals and application to partial differential inclusions,'' Nonlinear Anal., 43 (2001), 153-158.


    R. Livrea and S. A. Marano, On a min-max principle for non-smooth functions and applications, Commun. Appl. Anal., 13 (2009), 411-430.


    D. Motreanu and P. D. Panagiotopoulos, "Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities," Nonconvex Optimization and its Applications, 29, Kluwer Academic Publishers, Dordrecht, 1999.


    N. S. Papageorgiou and F. Papalini, Existence of two solutions for quasilinear periodic differential equations with discontinuities, Arch. Math. (Brno), 38 (2002), 285-296.


    B. Ricceri, Multiplicity of global minima for parametrized functions, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 21 (2010), 47-57.


    B. Ricceri, A class of nonlinear eigenvalue problems with four solutions, J. Nonlinear Convex Anal., 11 (2010), 503-511.

  • 加载中

Article Metrics

HTML views() PDF downloads(67) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint