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Three nonzero periodic solutions for a differential inclusion
1. | Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy, Italy |
References:
[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. |
[2] |
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. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
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. |
[7] |
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. |
[8] |
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. |
[9] |
R. Livrea and S. A. Marano, On a min-max principle for non-smooth functions and applications, Commun. Appl. Anal., 13 (2009), 411-430. |
[10] |
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. |
[11] |
N. S. Papageorgiou and F. Papalini, Existence of two solutions for quasilinear periodic differential equations with discontinuities, Arch. Math. (Brno), 38 (2002), 285-296. |
[12] |
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. |
[13] |
B. Ricceri, A class of nonlinear eigenvalue problems with four solutions, J. Nonlinear Convex Anal., 11 (2010), 503-511. |
show all references
References:
[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. |
[2] |
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. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
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. |
[7] |
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. |
[8] |
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. |
[9] |
R. Livrea and S. A. Marano, On a min-max principle for non-smooth functions and applications, Commun. Appl. Anal., 13 (2009), 411-430. |
[10] |
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. |
[11] |
N. S. Papageorgiou and F. Papalini, Existence of two solutions for quasilinear periodic differential equations with discontinuities, Arch. Math. (Brno), 38 (2002), 285-296. |
[12] |
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. |
[13] |
B. Ricceri, A class of nonlinear eigenvalue problems with four solutions, J. Nonlinear Convex Anal., 11 (2010), 503-511. |
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