Some degree calculations and applications to global bifurcation of variational inequalities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 37, Issue 4, 1999, Pages 473-500

  Le, Vy Khoi ^a  

^a MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; THEOREM PROVING; VARIATIONAL TECHNIQUES;

LERAY-SCHAUDER DEGREES; VARIATIONAL INEQUALITIES;

NONLINEAR EQUATIONS;

EID: 0033177636     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00062-5     Document Type: Article

References (27)

1. H. Brézis, Analyse Fonctionnelle, Paris, 1983.
2. F. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc. 9 (1983) 1-39.
3. E.N. Dancer, On the indices of fixed points of mappings in cones and applications, J. Math. Anal. Appl. 91 (1983) 131-151.
4. M. Degiovanni, Bifurcation problems for nonlinear elliptic variational inequalities, Ann. Fac. Sci. Toulouse 10 (1989) 215-258.
5. M. Degiovanni, A. Marino, Non-smooth variational bifurcation, Atti. Acc. Lincei Rend. Fis. 81 (1987) 259-270.
6. C. Do, The buckling of a thin elastic plate subjected to unilateral conditions, Lecture Notes in Mathematics, vol. 503, Springer, Berlin, 1976, pp. 307-316.
7. C. Do, Bifurcation theory for elastic plates subjected to unilateral conditions, J. Math. Anal. Appl. 60 (1977) 435-448.
8. P. Drábek, Solvability and Bifurcations of Nonlinear Equations, Longman Scientific and Technical Series, Longman, Essex, 1992.
9. D. Goeleven, V.H. Nguyen, M. Théra, Nonlinear eigenvalue problems governed by a variational inequality of von Karman's type: a degree theoretic approach, Topological Meth. Nonlinear Anal. 2 (1993) 253-276.
10. M.A. Krasnosels'kii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1963.
11. M. Kučera, A new method for obtaining eigenvalues of variational inequalities: operators with multiple eigenvalues, Czech. Math. J. 32 (1982) 197-207.
12. M. Kučera, A global continuation theorem for obtaining eigenvalues and bifurcation points, Czech. Math. J. 38 (1988) 120-137.
13. M. Kučera, J. Nečas, J. Souček, The eigenvalue problem for variational inequalities and a new version of the Ljusternik-Schnirelmann theory, Nonlinear Analysis, Academic Press, New York, 1978, pp. 125-143.
14. V.K. Le, Some global bifurcation results for variational inequalities, J. Differential Equations 131 (1996) 39-78.
15. V.K. Le, On global bifurcation of variational inequalities and applications, J. Differential Equations, to appear.
16. V.K. Le, Some global bifurcation results for elastic plates, J. Appl. Math. Comput., to appear.
17. V.K. Le, K. Schmitt, Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems, Appl. Math. Sci., vol. 123, Springer, New York, 1997.
18. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod Paris, 1969.
19. E. Miersemann, Über nichtlineare Eigenwertaufgaben in konvexen Mengen, Math. Nachr. 88 (1979) 191-205.
20. E. Miersemann, Eigenvalue problems for variational inequalities, Contemporary Math. 4 (1984) 25-43.
21. P. Quittner, Bifurcation points and eigenvalues of inequalities of reaction-diffusion type, J. Reine Angew. Math. 380 (1987) 1-13.
22. P. Quittner, Solvability and multiplicity results for variational inequalities, Comment. Math. Univ. Carolin. 30 (1989) 281-302.
23. P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Func. Anal. 7 (1971) 487-513.
24. C. Saccon, A global bifurcation result for variational inequalities, Bollettino U. M. I. 7-A (1993) 117-124.
25. F. Schuricht, Bifurcation from minimax solutions by variational inequalities, Math. Nachr. 154 (1991) 67-88.
26. F. Schuricht, Bifurcation from minimax solutions by variational inequalities in convex sets, Nonlinear Anal. TMA 26 (1996) 91-112.
27. A. Szulkin, Positive solutions of variational inequalities: a degree theoretic approach, J. Differential Equations 57 (1985) 90-111.