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2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS

Published online by Cambridge University Press:  01 September 2008

PASQUALE CANDITO ,
ROBERTO LIVREA  and
DUMITRU MOTREANU
PASQUALE CANDITO
Affiliation:
Dipartimento D.I.M.E.T, Facoltà di Ingegneria, Università di Reggio Calabria, Via Graziella, Località Feo di Vito, 89100 Reggio Calabria, Italy e-mail: pasquale.candito@unirc.it
ROBERTO LIVREA
Affiliation:
Dipartimento di Patrimonio Architettonico e Urbanistico, Facoltà di Architettura, Università di Reggio Calabria, Salita Melissari, 89100 Reggio Calabria, Italy e-mail: roberto.livrea@unirc.it
DUMITRU MOTREANU
Affiliation:
Département de Mathématiques, Université de Perpignan, Avenue de Villeneuve 52, 66860 Perpignan Cedex, France e-mail: motreanu@univ-perp.fr
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Abstract

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In this paper, some min–max theorems for even and C1 functionals established by Ghoussoub are extended to the case of functionals that are the sum of a locally Lipschitz continuous, even term and a convex, proper, lower semi-continuous, even function. A class of non-smooth functionals admitting an unbounded sequence of critical values is also pointed out.

Keywords

58E0549J35

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 3 , September 2008 , pp. 447 - 466
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Bartsch, T., Topological methods for variational problems with symmetries (Springer-Verlag, Berlin, Germany, 1993).CrossRefGoogle Scholar
2.Candito, P., Marano, S. A. and Motreanu, D., Critical pointy for a class of non-differentiable functions and applications, Discrete Contin. Dyn. Syst. 13 (2005), 175–194.CrossRefGoogle Scholar
3.Chang, K.-C., Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102–129.CrossRefGoogle Scholar
4.Clarke, F. H., Optimization and nonsmooth analysis, Classics Appl. Math. 5 (SIAM, Philadelphia, PA, 1990).CrossRefGoogle Scholar
5.Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, Germany, 1985).CrossRefGoogle Scholar
6.Ekeland, I., Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443–474.CrossRefGoogle Scholar
7.Goeleven, D., Motreanu, D., Dumont, Y. and Rochdi, M., Variational and hemivariational inequalities: Theory, methods and applications, Vol. I, Unilater analysis and unilater mechanics, Nonconvex Optim. Appl. 69 (Kluwer, Dordrecht, The Netherlands, 2003).CrossRefGoogle Scholar
8.Ghoussoub, N., Duality and perturbation methods in critical point theory, Cambridge Tracts Math. 107 (Cambridge University Press, Cambridge, UK, 1993).CrossRefGoogle Scholar
9.Livrea, R. and Marano, S. A., Existence and classification of critical points for non-differentiable functions, Adv. Differ. Equ. 9 (2004), 961–978.Google Scholar
10.Livrea, R., Marano, S. A. and Motreanu, D., Critical point for nondiferentiable functions in presence of splitting, J. Differ. Equ. 226 (2) (2006), 704–725.CrossRefGoogle Scholar
11.Marano, S. A. and Motreanu, D., A deformation theorem and some critical point results for non-differentiable functions, Topol. Methods Nonlinear Anal. 22 (2003), 139–158.CrossRefGoogle Scholar
12.Motreanu, D. and Panagiotopoulos, P. D., Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Nonconvex Optim. Appl. 29 (Kluwer, Dordrecht, The Netherlands, 1998).CrossRefGoogle Scholar
13.Panagiotopoulos, P. D., Hemivariational inequalities. Applications in mechanics and engineering (Springer-Verlag, Berlin, Germany, 1993).CrossRefGoogle Scholar
14.Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65 (Amer. Math. Soc., Providence, RI, 1986).CrossRefGoogle Scholar
15.Struwe, M., Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems, Second Edition, Ergeb. Math. Grenzgeb. 34(3) (Springer-Verlag, Berlin, Germany, 1996).Google Scholar
16.Szulkin, A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. Henri Poincaré 3 (1986), 77–109.CrossRefGoogle Scholar