Multibump solutions for a class of lagrangian systems slowly oscillating at infinity

Francesca Alessio; Piero Montecchiari

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 1, page 107-135
  • ISSN: 0294-1449

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Alessio, Francesca, and Montecchiari, Piero. "Multibump solutions for a class of lagrangian systems slowly oscillating at infinity." Annales de l'I.H.P. Analyse non linéaire 16.1 (1999): 107-135. <http://eudml.org/doc/78457>.

@article{Alessio1999,
author = {Alessio, Francesca, Montecchiari, Piero},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Lagrangian systems; Hamiltonian systems; homoclinic orbits; multibump solutions; minimax arguments},
language = {eng},
number = {1},
pages = {107-135},
publisher = {Gauthier-Villars},
title = {Multibump solutions for a class of lagrangian systems slowly oscillating at infinity},
url = {http://eudml.org/doc/78457},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Alessio, Francesca
AU - Montecchiari, Piero
TI - Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 1
SP - 107
EP - 135
LA - eng
KW - Lagrangian systems; Hamiltonian systems; homoclinic orbits; multibump solutions; minimax arguments
UR - http://eudml.org/doc/78457
ER -

References

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  1. [1] F. Alessio, Homoclinic solutions for second order systems with expansive time dependence, preprint, 1996. Zbl0881.34067MR1463919
  2. [2] A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of nonlinear Schrödinger equation, Arch. Rat. Mech. Anal., to appear. Zbl0896.35042
  3. [3] A. Ambrosetti and M.L. Bertotti, , Homoclinics for second order conservative systems, Partial differential equation and related subjects, Ed. M.Miranda, Pitman Research Notes in Math. Ser., 1992. Zbl0804.34046MR1190931
  4. [4] A. Ambrosetti and V. Coti Zelati, Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Padova, Vol. 89,1993, pp. 177-194. Zbl0806.58018MR1229052
  5. [5] U. Bessi, A Variational Proof of a Sitnikov-like Theorem, Nonlinear Anal. TMA, Vol. 20, 1993, pp. 1303-1318. Zbl0778.34036MR1220837
  6. [6] M.L. Bertotti and S. Bolotin, A variational approach for homoclinics in almost periodic Hamiltonian systems, Comm. Appl. Nonlinear Analysis, Vol. 2, 1995, pp. 43-57. Zbl0858.34039MR1355162
  7. [7] S. Bolotin, Existence of homoclinic motions, Vestnik Moskov. Univ. Ser. I Mat. MeKh., Vol.6, 1980, pp. 98-103. Zbl0549.58019MR728558
  8. [8] B. Buffoni and E. Séré, A global condition for quasi random behaviour in a class of conservative systems, preprint, 1995. Zbl0860.58027MR1374173
  9. [9] P. Caldiroli and P. Montecchiari, Homoclinics orbits for second order Hamiltonian systems with potential changing sign, Comm. Appl. Nonlinear Analysis, Vol. 1, 1994, pp. 97-129. Zbl0867.70012MR1280118
  10. [10] P. Caldiroli, P. Montecchiari and M. Nolasco, Asymptotic behaviour for a class of multibump solutions to Duffing-like systems, Proc. of the Workshop on Variational and Local Methods in the study of Hamiltonian systems, World Scientific, 1995. Zbl0951.37013MR1414014
  11. [11] K. Cieliebak and E. Séré, Pseudo-holomorphic curves and the shadowing Lemma, Duke Math. Journ., to appear. Zbl0955.37039
  12. [12] 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
  13. [13] V. Coti Zelati, P. Montecchiari and M. Nolasco, Multibump homoclinic solutions for a class of second order, almost periodic Hamiltonian systems, NODEA, to appear. Zbl0878.34045
  14. [14] V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., Vol. 4, 1991, pp. 693-727. Zbl0744.34045MR1119200
  15. [15] M. Del Pino and P.L. Felmer, Multipeak bound states for nonlinear Schrödinger equations, Ann. IHP Anal. Nonlinéaire, to appear. Zbl0901.35023MR1614646
  16. [16] C. Gui, Existence of multi-bump solutions for nonlinear Schrödinger equations via variational methods, Comm. in PDE, Vol. 21, 1996, pp. 787-820. Zbl0857.35116MR1391524
  17. [17] H. Hofer and K. Wysocki, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann., Vol. 228, 1990, pp. 483-503. Zbl0702.34039MR1079873
  18. [18] P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, part 1., part 2., Ann.IHP Anal. Nonlinéaire, Vol. 1, 1984, pp. 109-145, 223-283. Zbl0541.49009MR778970
  19. [19] C. Miranda, Un'osservazione su un teorema di Brouwer, Boll. Unione Mat. Ital., Vol. 3, 1940, pp. 5-7. Zbl0024.02203MR4775
  20. [20] P. Montecchiari, Existence and multiplicity of homoclinic solutions for a class of asymptotically periodic second order Hamiltonian systems, Ann. Mat. Pura Appl. (IV), Vol. 168, 1995, pp. 317-354. Zbl0849.34035MR1378249
  21. [21] P. Montecchiari, M. Nolasco and S. Terracini, Multiplicity of homoclinics for time recurrent second order systems, Calculus of Variations, to appear. Zbl0886.58014
  22. [22] P. Montecchiari, M. Nolasco and S. Terracini, A global condition for periodic Duffing-like equations, preprint, SISSA, 1995. Zbl0926.37005MR1487629
  23. [23] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh, Vol. 114 A, 1990, pp. 33-38. Zbl0705.34054MR1051605
  24. [24] P.H. Rabinowitz, Multibump solutions for an almost periodically forced singular Hamiltonian system, preprint, 1995. Zbl0828.34034MR1348521
  25. [25] P.H. Rabinowitz, A multibump construction in a degenerate setting, preprint, 1996. Zbl0876.34055MR1433175
  26. [26] P.H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., Vol 206, 1991, pp. 473-479. Zbl0707.58022MR1095767
  27. [27] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit., Vol. 209, 1991, pp. 27-42. Zbl0725.58017MR1143210
  28. [28] E. Séré, Looking for the Bernoulli shift, Ann. IHP Anal. Nonlinéaire, Vol. 10, 1993, pp. 561-590. Zbl0803.58013MR1249107
  29. [29] E. Serra, M. Tarallo and S. Terracini, On the existence of homoclinic solutions for almost periodic second order systems, Ann. IHP Anal. Nonlinéaire, to appear. Zbl0873.58032MR1420498
  30. [30] S. Wiggins, Global bifurcation and chaos, Applied Mathematical Sciences, Springer-Verlag, Vol. 73,1988. Zbl0661.58001

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