Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign

Mario Girardi; Michele Matzeu

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1993)

  • Volume: 4, Issue: 4, page 273-277
  • ISSN: 1120-6330

Abstract

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Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.

How to cite

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Girardi, Mario, and Matzeu, Michele. "Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 4.4 (1993): 273-277. <http://eudml.org/doc/244132>.

@article{Girardi1993,
abstract = {Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.},
author = {Girardi, Mario, Matzeu, Michele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Periodic solutions; Potentials changing sign; Second order nonautonomous systems; potentials changing sing; second order differential equations; periodic solutions},
language = {eng},
month = {12},
number = {4},
pages = {273-277},
publisher = {Accademia Nazionale dei Lincei},
title = {Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign},
url = {http://eudml.org/doc/244132},
volume = {4},
year = {1993},
}

TY - JOUR
AU - Girardi, Mario
AU - Matzeu, Michele
TI - Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1993/12//
PB - Accademia Nazionale dei Lincei
VL - 4
IS - 4
SP - 273
EP - 277
AB - Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.
LA - eng
KW - Periodic solutions; Potentials changing sign; Second order nonautonomous systems; potentials changing sing; second order differential equations; periodic solutions
UR - http://eudml.org/doc/244132
ER -

References

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  1. ALAMA, S. - TARANTELLO, G., On semilinear elliptic equations with indefinite nonlinearities. Arch. Rat. Mech. Analysis, to appear. Zbl0809.35022MR1383913DOI10.1007/BF01206962
  2. AMBROSETTI, A. - RABINOWITZ, P. H., Dual variational methods in critical point theory and applications. J. Funct. Anal., 14, 1973, 349-381. Zbl0273.49063MR370183
  3. BENNAOUM, A. K. - TROESTLER, C. - WILLEM, M., Existence and multiplicity results for homogeneous second order differential equations. J. Diff. Eq., to appear. Zbl0808.58013MR1287560DOI10.1006/jdeq.1994.1103
  4. YANHENG, DING - GIRARDI, M., Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign. Dynamical Systems and Applications, to appear. Zbl0771.34031MR1205441
  5. EKELAND, I., Convexity methods in Hamiltonian mechanics. Springer-Verlag, 1990. Zbl0707.70003MR1051888
  6. EKELAND, I. - HOFER, H., Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems. Invent. Math., 81, 1985, 155-188. Zbl0594.58035MR796195DOI10.1007/BF01388776
  7. GIRARDI, M. - MATZEU, M., Some multiplicity results for suhharmonic solutions to second order nonautonomous systems. Proceedings of the First World Congress of Nonlinear Analysis. Tompe, Florida, August 19-26 1992, to appear. Zbl0846.34033MR1389092
  8. HOFER, H., A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem. J. London Math. Soc., 31, (2), 1985, 566-570. Zbl0573.58007MR812787DOI10.1112/jlms/s2-31.3.566
  9. LASSOUED, L., Periodic solutions of a second order superquadratic system with change of sign of potential. J. Diff. Eq., 93, 1991, 1-18. Zbl0736.34041MR1122304DOI10.1016/0022-0396(91)90020-A
  10. RABINOWITZ, P. M., Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math., 31, 1978, 157-184. Zbl0358.70014MR467823

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