Literature cited
P. H. Rabinowitz, “Periodic solutions of Hamiltonian systems,” Commun. Pure Appl. Math.,31, 157–184 (1978).
V. Benci and P. H. Rabinowitz, “Critical point theorems for indefinite functionals,” Inventiones Math.,52, 336–352 (1979).
A. Capozzi, D. Fortunato, and A. Salvatore, “Periodic solutions of dynamical systems,” Meccanica-J. Ital. Assoc. Theoret. Appl. Mech., No. 4, 281–284 (1985).
A. I. Perov and V. L. Khatskevich, “On a variational approach in the investigation of periodic solutions of Hamiltonian systems,” in: Theory of Operators in Functional Spaces [in Russian], Voronezh (1983), pp. 72–79.
T. Ya. Azizov and I. S. Iokhvidov, Foundations of the Theory of Linear Operators in Spaces with an Indefinite Metric [in Russian], Nauka, Moscow (1986).
R. S. Phillips, “A minimax characterization of the eigenvalues of a positive symmetric operator in a space with an indefinite metric,” J. Fac. Sci. Univ. Tokyo Ser. A1,17, No. 1–2, 51–59 (1970).
B. Textorius, “Minimaxprinzipe zur Bestimmung der Eigenwerte J-nichtnegativer Operatoren,” Math. Scand.,35, No. 1, 101–114 (1974).
H. Langer, “Invariante Teilraume definisierbarer J-selbstadjungierter Operatoren,” Ann. Acad. Sci. Fenn Ser. A1, No. 475 (1971).
A. I. Perov, Variational Methods in the Theory of Nonlinear Oscillations [in Russian], Voronezh. State Univ. (1981).
A. I. Perov, T. I. Smagina, and V. L. Khatskevich, “A variational approach to the problem of periodic solutions,” Sib. Mat. Zh.,125, No. 1, 106–119 (1984).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 50, No. 4, pp. 3–9, October, 1991.
Rights and permissions
About this article
Cite this article
Azizov, T.Y., Khatskevich, V.L. Some applications of the theory of operators in Krein spaces to the solvability of nonlinear Hamiltonian systems. Mathematical Notes of the Academy of Sciences of the USSR 50, 987–992 (1991). https://doi.org/10.1007/BF01137724
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01137724