Existence and classification of critical points for nondifferentiable functions

Advances in Differential Equations

Volumn 9, Issue 9-10, 2004, Pages 961-978

  Livrea, Roberto ^a   Marano, Salvatore A ^a  

^a UNIVERSITY MEDITERRANEA OF REGGIO CALABRIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18144397044     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.
2. G. Barletta and S.A. Marano, The structure of the critical set in the mountain-pass theorem for nondifferentiable functions, Differential Integral Equations, 16 (2003), 1001-1012.
3. J. Chabrowski, "Variational Methods for Potential Operator Equations," de Gruyter Ser. Nonlinear Anal. Appl., 24, de Gruyter, Berlin, 1997.
4. K.-C. Chang, Variational methods for non-differentiable functionals, their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102-129.
5. F.H. Clarke, "Optimization and Nonsmooth Analysis," Classics Appl. Math., 5, SIAM, Philadelphia, 1990.
6. K. Deimling, "Nonlinear Functional Analysis," Springer-Verlag, Berlin, 1985.
7. I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc., 1 (1979), 443-474.
8. G. Fang, The structure of the critical set in the general mountain pass principle, Ann. Fac. Sci. Toulouse Math., 3 (1994), 345-362.
9. G. Fang, On the existence and the classification of critical points for non-smooth functionals, Can. J. Math., 47 (1995), 684-717.
10. N. Ghoussoub, A min-max principle with a relaxed boundary condition, Proc. Amer. Math. Soc., 117 (1993), 439-447.
11. N. Ghoussoub, "Duality and Perturbation Methods in Critical Point Theory," Cambridge Tracts in Math., 107, Cambridge Univ. Press, Cambridge, 1993.
12. N. Ghoussoub and D. Preiss, A general mountain pass principle for locating and classifying critical points, Ann. Inst. H. Poincaré Anal. Non Linéaire, 6 (1989), 321- 330.
13. C. Kuratowski, "Topology," Vol. II, Academic Press, New York, 1968.
14. C. Lefter, Critical point theorems for lower semicontinuous functionals, An. Ştiinţ. Univ. Al. I. Cuza Ia̧si Secţ. I a Mat., 47 (2001), 189-198.
15. S.A. Marano and D. Motreanu, A deformation theorem and some critical point results for non-differentiable functions, Topol. Methods Nonlinear Anal., 22 (2003), 139-158.
16. D. Motreanu, On the proof of a minimax principle, Matematiche (Catania), to appear.
17. D. Motreanu and P.D. Panagiotopoulos, "Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities," Nonconvex Optim. Appl., 29, Kluwer, Dordrecht, 1998.
18. P.D. Panagiotopoulos, "Hemivariational Inequalities. Applications in Mechanics and Engineering," Springer-Verlag, Berlin, 1993.
19. P. Pucci and J. Serrin, Extensions of the mountain pass theorem, J. Funct. Anal., 59 (1984), 185-210.
20. P. Pucci and J. Serrin, The structure of the critical set in the mountain pass theorem, Trans. Amer. Math. Soc., 299 (1987), 115-132.
21. V. Radulescu, Mountain pass theorem for non-differentiable functions and applications, Proc. Japan Acad. Ser. A Math. Sci., 69 (1993), 193-198.
22. E.H. Spanier, "Algebraic Topology," McGraw-Hill, New York, 1966.
23. M. Struwe, "Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems," Second Edition, Ergeb. Math. Grenzgeb., 34, Springer-Verlag, Berlin, 1996.
24. A. Szulkin, Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. Henri Poincaré, 3 (1986), 77-109.