On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign
Matzeu, M. ; Girardi, M.
Rendiconti del Seminario Matematico della Università di Padova, Tome 98 (1997), p. 193-210 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{RSMUP_1997__97__193_0,
     author = {Matzeu, M. and Girardi, M.},
     title = {On periodic solutions of a class of second order nonautonomous systems with nonhomogeneous potentials indefinite in sign},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {98},
     year = {1997},
     pages = {193-210},
     mrnumber = {1476171},
     zbl = {0891.34050},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1997__97__193_0}
}

Matzeu, M.; 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, Tome 98 (1997) pp. 193-210. http://gdmltest.u-ga.fr/item/RSMUP_1997__97__193_0/

[1] A. Ambrosetti - P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), pp. 349-381. | MR 370183 | Zbl 0273.49063

[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. | MR 1397350 | Zbl 1013.34038

[3] F. Antonacci, Existence of periodic solutions of Hamiltonian systems with potential indefinite in sign, to appear on Nonlinear Analysis. | MR 1484908 | Zbl 0894.34036

[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. | MR 1287560 | Zbl 0837.34029 | Zbl 0808.58013

[5] H. Brezis, Analyse fonctionelle: théorie et applications, Masson (1983). | MR 697382 | Zbl 0511.46001

[6] P. Caldiroli - P. MONTECCHIARI, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potential, Comm. Appl. Nonlinear Anal., 1 (1994), pp. 97-129. | MR 1280118 | Zbl 0867.70012

[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. | MR 1205441 | Zbl 0771.34031

[8] I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Springer-Verlag (1990). | MR 1051888 | Zbl 0707.70003

[9] I. Ekeland - H. HOFER, Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems, Inv. Math., 81 (1985), pp. 155-188. | MR 796195 | Zbl 0594.58035

[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. | MR 1322202 | Zbl 0821.34041

[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. | MR 1269617 | Zbl 0799.58064

[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. | MR 812787 | Zbl 0573.58007

[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. | MR 1080211 | Zbl 0724.34051

[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. | MR 1122304 | Zbl 0736.34041