On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign

M. Matzeu; M. Girardi

Rendiconti del Seminario Matematico della Università di Padova (1997)

  • Volume: 97, page 193-210
  • ISSN: 0041-8994

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Matzeu, M., and Girardi, M.. "On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign." Rendiconti del Seminario Matematico della Università di Padova 97 (1997): 193-210. <http://eudml.org/doc/108423>.

@article{Matzeu1997,
author = {Matzeu, M., Girardi, M.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {periodic solutions; nonhomogeneous potential; critical points; Morse index},
language = {eng},
pages = {193-210},
publisher = {Seminario Matematico of the University of Padua},
title = {On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign},
url = {http://eudml.org/doc/108423},
volume = {97},
year = {1997},
}

TY - JOUR
AU - Matzeu, M.
AU - Girardi, M.
TI - On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1997
PB - Seminario Matematico of the University of Padua
VL - 97
SP - 193
EP - 210
LA - eng
KW - periodic solutions; nonhomogeneous potential; critical points; Morse index
UR - http://eudml.org/doc/108423
ER -

References

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  1. [1] A. Ambrosetti - P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), pp. 349-381. Zbl0273.49063MR370183
  2. [2] F. Antonacci, Periodic and homoclinic solutions to a class of Hamiltonian systems with indefinite potential in sign, to appear on Boll. Un. Mat. Ital. Zbl1013.34038MR1397350
  3. [3] F. Antonacci, Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign, to appear on Nonlinear Analysis. Zbl0894.34036MR1484908
  4. [4] A.K. Ben Naoum - C. Troestler - M. Willem, Existence and multiplicity results for homogeneous second order differential equations, to appear on J. Diff. E q. Zbl0808.58013MR1287560
  5. [5] H. Brezis, Analyse fonctionelle: théorie et applications, Masson (1983). Zbl0511.46001MR697382
  6. [6] P. Caldiroli - P. MONTECCHIARI, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potential, Comm. Appl. Nonlinear Anal., 1 (1994), pp. 97-129. Zbl0867.70012MR1280118
  7. [7] Y.H. Ding - M. Girardi, Periodic and homoclinic solutions to a class of Hamiltonian systems with the potential changing sign, Dynamical Syst. Appl., 2 (1993), pp. 131-145. Zbl0771.34031MR1205441
  8. [8] I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Springer-Verlag (1990). Zbl0707.70003MR1051888
  9. [9] I. Ekeland - H. HOFER, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Inv. Math., 81 (1985), pp. 155-188. Zbl0594.58035MR796195
  10. [10] M. Girardi - M. Matzeu, Existence and multiciplity results for periodic solutions of superquadratic Hamiltonian systems where the potential changes sign, Nonlinear Diff. Eq. and Appl., 2 (1995), pp. 35-61. Zbl0821.34041MR1322202
  11. [11] M. Girardi - M. Matzeu, Periodic solutions of second order nonautonomous systems with the potential changing sign, Rend. Mat. Acc. Lincei, s. 9, v. 4 (1993), pp. 273-277. Zbl0799.58064MR1269617
  12. [12] H. Hofer, A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem, J. London Math. Soc. (2), 31 (1985), pp. 566-570. Zbl0573.58007MR812787
  13. [13] L. Lassoued, Solutions periodiques d'un systeme differential non lineaire du second ordre avec changement de sign, Ann. Math. Pura Appl., 156 (1990), pp. 76-111. Zbl0724.34051MR1080211
  14. [14] L. Lassoued, Periodic solutions of a second order superquadratic system with change of sign of the potential, J. Diff. Eq., 93 (1991), 1-18. Zbl0736.34041MR1122304

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