Lagrangian systems in the presence of singularities
HTML articles powered by AMS MathViewer
- by A. Capozzi, C. Greco and A. Salvatore PDF
- Proc. Amer. Math. Soc. 102 (1988), 125-130 Request permission
Abstract:
In this paper we study dynamical systems embedded in a conservative field of forces, whose potential is "singular." We look for $T$-periodic solutions of these systems by variational methods.References
- V. Benci, Normal modes of a Lagrangian system constrained in a potential well, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 5, 379–400 (English, with French summary). MR 779875
- V. Benci, A. Capozzi, and D. Fortunato, Periodic solutions of Hamiltonian systems with superquadratic potential, Ann. Mat. Pura Appl. (4) 143 (1986), 1–46 (English, with Italian summary). MR 859596, DOI 10.1007/BF01769209
- A. Capozzi, D. Fortunato, and A. Salvatore, Periodic solutions of Lagrangian systems with bounded potential, J. Math. Anal. Appl. 124 (1987), no. 2, 482–494. MR 887004, DOI 10.1016/0022-247X(87)90009-6
- A. Capozzi and A. Salvatore, Periodic solutions of Hamiltonian systems: the case of the singular potential, Nonlinear functional analysis and its applications (Maratea, 1985) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 173, Reidel, Dordrecht, 1986, pp. 207–216. MR 852580, DOI 10.1016/0010-4485(85)90243-x F. Giannoni, Soluzioni periodiche di sistemi Hamiltoniani in presenza di vincoli, Pubbl. Dip. Mat. Univ. Pisa 11 (1983).
- William B. Gordon, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975), 113–135. MR 377983, DOI 10.1090/S0002-9947-1975-0377983-1
- William B. Gordon, A minimizing property of Keplerian orbits, Amer. J. Math. 99 (1977), no. 5, 961–971. MR 502484, DOI 10.2307/2373993 C. Greco, Remarks on periodic solutions of second order Hamiltonian systems in an unbounded potential well, Nonlinear Oscillation for Conservative Systems, Proc. Venice, January 1985 (A. Ambrosetti), Pitagora Ed., Bologna, 1985, pp. 37-41.
- J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations, J. Differential Equations 52 (1984), no. 2, 264–287. MR 741271, DOI 10.1016/0022-0396(84)90180-3
- Addolorata Salvatore, Periodic solution of Hamiltonian systems with a subquadratic potential, Boll. Un. Mat. Ital. C (6) 3 (1984), no. 1, 393–406 (English, with Italian summary). MR 749296
Similar Articles
- Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F22,, 34C25,58E05,70H35
- Retrieve articles in all journals with MSC: 58F22,, 34C25,58E05,70H35
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 125-130
- MSC: Primary 58F22,; Secondary 34C25,58E05,70H35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915729-0
- MathSciNet review: 915729