On Global Bifurcation of Variational Inequalities and Applications

Journal of Differential Equations

Volumn 141, Issue 2, 1997, Pages 254-294

  Le, Vy Khoi ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000888686     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3328     Document Type: Article

References (33)

1. Amann H. Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18:1976;620-709.
2. Brézis H. Analyse fonctionnelle. 1983;Masson, Paris.
3. Browder F. Fixed point theory and nonlinear problems. Bull. Amer. Math. Soc. 9:1983;1-39.
4. Dancer E. N. On the indices of fixed points of mappings in cones and applications. J. Math. Anal. Appl. 91:1983;131.
5. Degiovanni M. Bifurcation problems for nonlinear elliptic variational inequalities. Ann. Fac. Sci. Toulouse. 10:1989;215-258.
6. Degiovanni M., Marino A. Non-smooth variational bifurcation. Atti. Acc. Linei Rend. Fis. 81:1987;259-270.
7. Do C. Bifurcation theory for elastic plates subjected to unilateral conditions. J. Math. Anal. Appl. 60:1977;435-448.
8. Drábek P. Solvability and Bifurcations of Nonlinear Equations. Longman Scientific and Technical Series. 1992.
9. Gilbarg D., Trudinger N. Elliptic Partial Differential Equations of Second Order. 1983;Springer-Verlag, Berlin.
10. Krasnosels'kii M. A. Topological Methods in the Theory of Nonlinear Integral Equations. 1963;Pergamon Press, Oxford.
11. Kučera M. Bifurcation points of variational inequalities. Czech. Math. J. 32:1982;208-226.
12. Kučera M. A new method for obtaining eigenvalues of variational inequalities: Operators with multiple eigenvalues. Czech. Math. J. 32:1982;197-207.
13. Kučera M. A global continuation theorm for obtaining eigenvalues and bifurcation points. Czech. Math. J. 38:1988;120-137.
14. Le V. K. Some global bifurcation results for variational inequalities. J. Diff. Eq. 131:1996;39-78.
15. V. K. Le, Some global bifurcation results for elastic plates, J. Appl. Math. Comp.
16. V. K. Le, K. Schmitt, Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems, Springer-Verlag, New York.
17. Lions J. L. Quelques méthodes de résolution des problèmes aux limites non linéaires. 1969;Dunod, Paris.
18. McLeod J. B., Turner R. E. L. Bifurcation for nondifferentiable operators with an application to elasticity. Arch. Rational Mech. Anal. 63:1976;1-45.
19. Miersemann E. Über positive Lösungen von Eigenwertgleichungen mit Anwendungen auf elliptische Gleichungen zweiter Ordnung und auf ein Beulproblem für die Platte. ZAMM. 59:1979;189-194.
20. Miersemann E. Eigenvalue problems for variational inequalities. Contemp. Math. 4:1984;25-43.
21. Oden J. T., Martins J. A. C. Models and computational methods for dynamic friction phenomena. Comp. Meth. Appl. Mech. Eng. 52:1985;527-634.
22. Pascali D., Sburlan J. Nonlinear Mappings of Monotone Type. 1978;Sijthoff and Noordhoff, Bucharest.
23. P. Quittner, 1986, Spectral analysis of variational inequalities, 27, 605, 629.
24. Quittner P. Solvability and multiplicity results for variational inequalities. Comment. Math. Univ. Carolin. 30:1989;281-302.
25. Rabier P. J., Oden J. T. Solution to Signorini-like contact problems through interface models, I preliminaries and formulation of a variational equality. Nonlinear Anal. TMA. 11:1987;1325-1350.
26. Rabier P. J., Oden J. T. Solution to Signorini-like contact through interface models, II, existence and uniqueness theorems. Nonlinear Anal. TMA. 12:1988;1-17.
27. Rabinowitz P. Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7:1971;487-513.
28. Schmitt K. Analysis Methods for the Study of Nonlinear Equations. 1993;University of Utah Lecture Notes.
29. Schuricht F. Bifurcation from minimax solutions by variational inequalities. Math. Nachr. 154:1991;67-88.
30. Schuricht F. Bifurcation from minimax solutions by variational inequalities in convex sets. Nonlinear Anal. TMA. 26:1996;91-112.
31. Szulkin A. Positive solutions of variational inequalities: a degree theoretic approach. J. Diff. Eq. 57:1985;90-111.
32. Szulkin A. Existence and nonuniqueness of solutions of a noncoercive elliptic variational inequality. Proc. Symp. Pure Math. 45:1986;413-418.
33. Trojanski S. L. On locally uniformly convex and differentiable norms in certain nonseparable Banach spaces. Studia Math. 37:1971;173-180.