The principle of symmetric criticality for non-differentiable mappings

Journal of Functional Analysis

Volumn 214, Issue 2, 2004, Pages 428-449

  Kobayashi, Jun ^a   Ôtani, Mitsuharu ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

Elliptic variational inequality; Group action; Non smooth functional; Subdifferential operator; Symmetric criticality

Indexed keywords

EID: 4344599726     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2004.04.006     Document Type: Article

References (26)

1. Akagi G. Kobayashi J. Ôtani M. Principle of symmetric criticality and evolution equations, in: W. Feng, X. Lu (Eds.), Dynamical Systems and Differential Equations (Proc. Wilmington, 2002), expanded volume of Discrete Contin. Dyn. Syst. 2003, pp. 1-10
2. Asakawa H. Accretivity and duality map in Banach space Proc. Japan Acad. Ser. A Math. Sci. 60 1984 201-204
3. Asakawa H. Restriction of maximal monotone operator to closed linear subspace TRU Math. (SUT J. Math.) 23 1987 97-116
4. Asplund E. Averaged norms Israel J. Math. 5 1967 227-233
5. Barbu V. Nonlinear Semigroups and Differential Equations in Banach spaces 1976 Noordhoff Leiden
6. Beauzamy B. Introduction to Banach Spaces and their Geometry 2nd Edition 1985 North-Holland Amsterdam
7. Brézis H. Analyse Fonctionnelle 1983 Masson Paris
8. Brézis H. Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations in: Zarantonello E. (Ed.), Contributions to Nonlinear Functional Analysis 1971 101-156 Academic Press New York
9. Brézis H. Crandall M. Pazy A. Perturbations of nonlinear maximal monotone sets in Banach spaces Comm. Pure Appl. Math. 23 1970 123-144
10. Cioranescu I. Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems 1990 Kluwer Academic Publishers Dordrecht
11. Coleman S. Classical lumps and their quantum descendants, in: A. Zichichi (Ed.), New Phenomena in Subnuclear Physics Part A, (Proc. Sicily 1975), Plenum Press, Yew York, 1977, pp. 297-421
12. D́az J.I. On a free boundary problem arising in climatology Kenmochi N. Free Boundary Problems: Theory and Applications II, (Proc. Chiba 1999) 2000 92-109 Gakkotosho Tokyo
13. Duvaut G. Lions J.L. Les Inéquations en Mécanique et en Physique 1972 Dunod Paris
14. Kalashnikov A.S. Some problem of the qualitative theory of second-order nonlinear degenerate parabolic equations Russian Math. Surveys 42:2 1987 169-222
15. Kelley J. Namioka I. Linear Topological Spaces 2nd Edition 1976 Springer New York
16. Köthe G. Topological Vector Spaces I 1969 Springer Berlin
17. Krawciewicz W. Marzantowicz W. Some remarks on the Lusternik-Schnirelman method for nondifferentiable functionals invariant with respect to a finite group action Rocky Mountain J. Math. 20 1990 1041-1049
18. Palais R.S. The principle of symmetric criticality Comm. Math. Phys. 69 1979 19-30
19. Pauli W. Theory of Relativity 1958 Pergamon Press London
20. Rudin W. Functional Analysis 1973 Tata McGraw-Hill New Delhi
21. Suzuki T. Nagasaki K. Lifting of local subdifferentiations and elliptic boundary value problems on symmetric domains Proc. Japan Acad. Ser. A Math. Sci. 64 1988 1-7
22. Suzulkin A. Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems Ann. Inst. H. Poincaré Anal. Non Linéaire 3 1986 77-109
23. Vanderbauwhede A. Local Bifurcation and Symmetry 1982 Pitman Advanced Publishing Program Boston
24. Varga C. Dályai Z. An existence result for a class of hemivariational inequalities, preprint
25. Weyl H. Space-Time-Matter 1951 Dover New York
26. Willem M. Minimax Theorems 1996 Birkäuser Boston