Multiple critical points for indefinite functionals and applications

Journal of Differential Equations

Volumn 155, Issue 1, 1999, Pages 203-230

  Candela, Anna Maria ^a   Giannoni, Fabio ^b   Masiello, Antonio ^a  

^a UNIVERSITY OF BARI   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033542303     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3572     Document Type: Article

References (25)

1. Benci V., Fortunato D. Periodic trajectories for the Lorentz metric of a static gravitational field. Variational Methods (Proc. Conf., Paris, 1988). Progr. Nonlinear Differential Equations Appl. 4:1990;Birkhäuser. p. 413-429.
2. Benci V., Fortunato D. On the existence of infinitely many geodesics on spacetime manifolds. Adv. Math. 105:1994;1-25.
3. Benci V., Fortunato D., Giannoni F. On the existence of multiple geodesics in static space-times. Ann. Inst. H. Poincaré Anal. Non Linéaire. 8:1991;79-102.
4. Benci V., Fortunato D., Masiello A. On the geodesic connectedeness of Lorentzian manifolds. Math. Z. 217:1994;73-93.
5. E. Fadell, Lectures in Cohomological Index Theories of G-spaces with Applications to Critical Point Theory, Raccolta di seminari, Università della Calabria, 1985.
6. Fadell E., Husseini S. Category of loop spaces of open subsets in Euclidean space. Nonlinear Anal. 12:1991;1153-1161.
7. Fadell E., Husseini S. Infinite cuplengh in free loop spaces with an application to a problem of the N-body type. Ann. Inst. H. Poincaré Anal. Non Linéaire. 9:1992;305-319.
8. Fadell E., Husseini S. Relative category, products and coproducts. Rend. Sem. Mat. Fis. Milano. 64:1994;99-115.
9. Fournier G., Lupo D., Ramos M., Willem M. Limit relative category and critical point theory. Dynamics Reported. 1994;Springer-Verlag, Berlin. p. 1-24.
10. Fournier G., Willem M. Relative category and the calculus of variations. Variational Methods (Proc. Conf., Paris, 1988). Progr. Nonlinear Differential Equations Appl. 4:1990;Birkhäuser, Basel. p. 95-104.
11. Giannoni F. Periodic solutions of dynamical systems by a Saddle Point Theorem of Rabinowitz. Nonlinear Anal. 13:1989;707-719.
12. Giannoni F., Masiello A. Geodesics on product Lorentzian manifolds. Ann. Inst. H. Poincaré Anal. Non Linéaire. 12:1995;27-60.
13. Greco C. Periodic trajectories in static space-times. Proc. Roy. Soc. Edinburgh Sect. A. 113:1989;99-103.
14. Greco C. Periodic trajectories for a class of Lorentz metrics of a time-dependent gravitational field. Math. Ann. 287:1990;515-521.
15. Greco C. Multiple periodic trajectories on stationary space-times. Ann. Mat. Pura Appl. (4). 162:1992;337-348.
16. Klingenberg W. Lectures on Closed Geodesics. 1978;Springer-Verlag, Berlin.
17. Masiello A. Timelike periodic trajectories in stationary Lorentzian manifolds. Nonlinear Anal. 19:1992;531-545.
18. Masiello A. On the existence of a timelike trajectory for a Lorentzian metric. Proc. Roy. Soc. Edinburgh Sect. A. 125:1995;807-815.
19. Palais R. S. Lusternik-Schnirelman theory on Banach manifolds. Topology. 5:1966;115-132.
20. Piccione P., Sampalmieri R. Geodesical connectedeness of compact Lorentzian manifolds. Dynam. Systems Appl. 5:1996;479-502.
21. Rabinowitz P. H. A minimax principle and applications to elliptic partial differential equations. Proc. Nonlinear Partial Differential Equations. Lecture Notes in Math. 648:1978;Springer-Verlag, New York. p. 97-115.
22. Rabinowitz P. H. Minimax methods in critical point theory with applications to differential equations. Reg. Conf. Series Math. Amer. Math. Soc. 65:1988;Providence.
23. Silva E. A. de B. e. Linking theorems and applications to semilinear elliptic problems at resonance. Nonlinear Anal. 16:1991;455-477.
24. Struwe M. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. 1990;Springer-Verlag, Berlin.
25. Szulkin A. A relative category and applications to critical point theory for strongly indefinite functionals. Nonlinear Anal. 15:1990;725-739.