Geodesic
2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 447-466

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089508004333
Mots-clés : 58E05, 49J35 
CANDITO, PASQUALE; LIVREA, ROBERTO; MOTREANU, DUMITRU. 2-SYMMETRIC CRITICAL POINT THEOREMS FOR NON-DIFFERENTIABLE FUNCTIONS. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 447-466. doi: 10.1017/S0017089508004333
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     title = {2-SYMMETRIC {CRITICAL} {POINT} {THEOREMS} {FOR} {NON-DIFFERENTIABLE} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004333/}
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[1] 1.Bartsch, T., Topological methods for variational problems with symmetries (Springer-Verlag, Berlin, Germany, 1993). Google Scholar | DOI

[2] 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. Google Scholar | DOI

[3] 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. Google Scholar | DOI

[4] 4.Clarke, F. H., Optimization and nonsmooth analysis, Classics Appl. Math. (SIAM, Philadelphia, PA, 1990). Google Scholar | DOI

[5] 5.Deimling, K., Nonlinear functional analysis (Springer-Verlag, Berlin, Germany, 1985). Google Scholar | DOI

[6] 6.Ekeland, I., Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443–474. Google Scholar | DOI

[7] 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. (Kluwer, Dordrecht, The Netherlands, 2003). Google Scholar | DOI

[8] 8.Ghoussoub, N., Duality and perturbation methods in critical point theory, Cambridge Tracts Math. (Cambridge University Press, Cambridge, UK, 1993). Google Scholar | DOI

[9] 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] 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. Google Scholar | DOI

[11] 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. Google Scholar | DOI

[12] 12.Motreanu, D. and Panagiotopoulos, P. D., Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Nonconvex Optim. Appl. (Kluwer, Dordrecht, The Netherlands, 1998). Google Scholar | DOI

[13] 13.Panagiotopoulos, P. D., Hemivariational inequalities. Applications in mechanics and engineering (Springer-Verlag, Berlin, Germany, 1993). Google Scholar | DOI

[14] 14.Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. (Amer. Math. Soc., Providence, RI, 1986). Google Scholar | DOI

[15] 15.Struwe, M., Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems, Second Edition, Ergeb. Math. Grenzgeb. (3) (Springer-Verlag, Berlin, Germany, 1996). Google Scholar

[16] 16.Szulkin, A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. Henri Poincaré 3 (1986), 77–109. Google Scholar | DOI

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