On the existence of homoclinic solutions for almost periodic second order systems

Enrico Serra; Massimo Tarallo; Susanna Terracini

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 6, page 783-812
  • ISSN: 0294-1449

How to cite

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Serra, Enrico, Tarallo, Massimo, and Terracini, Susanna. "On the existence of homoclinic solutions for almost periodic second order systems." Annales de l'I.H.P. Analyse non linéaire 13.6 (1996): 783-812. <http://eudml.org/doc/78401>.

@article{Serra1996,
author = {Serra, Enrico, Tarallo, Massimo, Terracini, Susanna},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {homoclinic solution; second order Lagrangian},
language = {eng},
number = {6},
pages = {783-812},
publisher = {Gauthier-Villars},
title = {On the existence of homoclinic solutions for almost periodic second order systems},
url = {http://eudml.org/doc/78401},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Serra, Enrico
AU - Tarallo, Massimo
AU - Terracini, Susanna
TI - On the existence of homoclinic solutions for almost periodic second order systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 6
SP - 783
EP - 812
LA - eng
KW - homoclinic solution; second order Lagrangian
UR - http://eudml.org/doc/78401
ER -

References

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  1. [1] A. Ambrosetti and M.L. Bertotti, Homoclinics for second order conservative systems, Preprint SNS, 1991. Zbl0804.34046MR1190931
  2. [2] A. Ambrosetti and V. Coti Zelati, Multiple homoclinic orbits for a class of conservative systems, Preprint SNS, 1992. Zbl0780.49008
  3. [3] M.L. Bertotti and S.V. Bolotin, Homoclinic solutions of quasiperiodic Lagrangian systems, Preprint, Università di Trento, 1994. Zbl0827.34037MR1347977
  4. [4] S.V. Bolotin, The existence of homoclinic motions, Vestnik Moskow Univ. Ser I Math. Mekh., Vol. 6, 1980, pp. 98-103. Zbl0549.58019MR728558
  5. [5] P. Caldiroli and P. Montecchiari, Homoclinic orbits for second order Hamiltonian Systems with potential changing sign, Preprint, SISSA, 1994. Zbl0867.70012MR1280118
  6. [6] P. Montecchiari, Existence and multiplicity of homoclinic solutions for a class of asymptotically periodic second order Hamiltonian Systems, Preprint, SISSA, 1993. Zbl0802.34052MR1269616
  7. [7] V. Coti Zelati, I. Ekeland and E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann., Vol. 288, 1990, pp. 133-160. Zbl0731.34050MR1070929
  8. [8] V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, Jour. of AMS, Vol. 4, 1991 pp. 693-727. Zbl0744.34045MR1119200
  9. [9] B.M. Levitan and V.V. Zhikov, Almost periodic functions and differential equations, (Cambridge University Press, ed.), 1982 Zbl0499.43005MR690064
  10. [10] K.R. Meyer and G. Sell, Homoclinic orbits and Bernoulli bundles in almost periodic systems, Oscillations, bifurcations and chaos (Amer. Math. Soc., Providence, R.I., ed.), 1987. Zbl0636.34037MR909934
  11. [11] K.R. Meyer and G. Sell, Melnikov transforms, Bernoulli bundles and almost periodic perturbations, Trans. AMS, Vol. 314, 1989, pp. 63-105. Zbl0707.34041MR954601
  12. [12] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh, Vol. 114A, 1990, pp. 33-38. Zbl0705.34054MR1051605
  13. [13] P.H. Rabinowitz, Homoclinic and heteroclinic orbits for a class of Hamiltonian system, Calc. Var. and PDE, Vol. 1, 1993, pp. 1-36. Zbl0791.34042MR1261715
  14. [14] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit., Vol. 209, 1991, pp. 27-42. Zbl0725.58017MR1143210
  15. [15] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré, Anal. Non Linéaire, Vol. 10, 1993, pp. 561-590. Zbl0803.58013MR1249107
  16. [16] E. Séré, Homoclinic orbits on compact hypersurfaces in R of restricted contact type, Preprint CEREMADE, 1992. 

Citations in EuDML Documents

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  1. Gregory S. Spradlin, Scattered homoclinics to a class of time-recurrent Hamiltonian systems
  2. Francesca Alessio, Marta Calanchi, Homoclinic-type solutions for an almost periodic semilinear elliptic equation on R n
  3. Vittorio Coti Zelati, Margherita Nolasco, Multibump solutions for Hamiltonian systems with fast and slow forcing
  4. Gregory S. Spradlin, An elliptic equation with no monotonicity condition on the nonlinearity
  5. Francesca Alessio, Piero Montecchiari, Multibump solutions for a class of lagrangian systems slowly oscillating at infinity

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