Homoclinics : Poincaré-Melnikov type results via a variational approach

Antonio Ambrosetti; Marino Badiale

Annales de l'I.H.P. Analyse non linéaire (1998)

  • Volume: 15, Issue: 2, page 233-252
  • ISSN: 0294-1449

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Ambrosetti, Antonio, and Badiale, Marino. "Homoclinics : Poincaré-Melnikov type results via a variational approach." Annales de l'I.H.P. Analyse non linéaire 15.2 (1998): 233-252. <http://eudml.org/doc/78437>.

@article{Ambrosetti1998,
author = {Ambrosetti, Antonio, Badiale, Marino},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {critical point theory; existence of homoclinics; doubly-asymptotic solutions; perturbed differential equations; Poincaré-Melnikov like results; multiplicity results; second-order Hamiltonian system; perturbed radial systems; existence of semiclassical states; Schrödinger equations with potential; forced Schrödinger equations},
language = {eng},
number = {2},
pages = {233-252},
publisher = {Gauthier-Villars},
title = {Homoclinics : Poincaré-Melnikov type results via a variational approach},
url = {http://eudml.org/doc/78437},
volume = {15},
year = {1998},
}

TY - JOUR
AU - Ambrosetti, Antonio
AU - Badiale, Marino
TI - Homoclinics : Poincaré-Melnikov type results via a variational approach
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1998
PB - Gauthier-Villars
VL - 15
IS - 2
SP - 233
EP - 252
LA - eng
KW - critical point theory; existence of homoclinics; doubly-asymptotic solutions; perturbed differential equations; Poincaré-Melnikov like results; multiplicity results; second-order Hamiltonian system; perturbed radial systems; existence of semiclassical states; Schrödinger equations with potential; forced Schrödinger equations
UR - http://eudml.org/doc/78437
ER -

References

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  7. [7] S.V. Bolotin, Homoclinic orbits to invariant tori of Hamiltonian systems, A.M.S. Transl., Vol. 168, 1995, pp. 21-90. Zbl0847.58024
  8. [8] 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
  9. [9] V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for a second order Hamiltonian systems possessing superquadratic potentials. Jour. Am. Math. Soc., Vol. 4, 1991, pp. 693-727. Zbl0744.34045MR1119200
  10. [10] V.V. Kozlov, Integrability and non-integrability in Hamiltonian Mechanics. Russian Math. Surveys, Vol. 38, 1983, pp. 1-76. Zbl0525.70023
  11. [11] U. Kirchgraber and D. Stoffer, Chaotic behaviour in simple dynamical systems, SIAM Review, Vol. 32, 1990, pp. 424-452. Zbl0715.58024MR1069896
  12. [12] L. Jeanjean, Two positive solutions for a class of nonhomogeneous elliptic equations, preprint. Zbl0890.35048MR1741765
  13. [13] S. Mathlouti, Bifurcation d'horbites homoclines pour les systèmes hamiltoniens. Ann. Fac. Sciences Toulouse, Vol. 1, 1992, pp. 211-235. Zbl0780.58034
  14. [14] V.K. Melnikov, On the stability of the center for time periodic perturbations, Trans. Moscow Math. Soc., Vol. 12, 1963, pp. 3-52. Zbl0135.31001MR156048
  15. [15] H. Poincaré, Les Méthodes nouvelles de la méchanique céleste., 1892. Zbl25.1847.03
  16. [16] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., Vol. 209, 1992, pp. 27-42. Zbl0725.58017MR1143210
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Citations in EuDML Documents

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  1. A. Ambrosetti, D. Arcoya, J. L. Gámez, Asymmetric bound states of differential equations in nonlinear optics
  2. Matthias Schneider, Prescribing scalar curvature on S 3
  3. Andrea Malchiodi, Some existence results for the scalar curvature problem via Morse theory
  4. S. Alama, A. J. Berlinsky, L. Bronsard, Minimizers of the Lawrence–Doniach energy in the small-coupling limit : finite width samples in a parallel field
  5. Marta Macrì, Soluzioni omocline a varietà invarianti: un approccio variazionale
  6. Antonio Ambrosetti, Veronica Felli, Andrea Malchiodi, Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity
  7. Matteo Novaga, Enrico Valdinoci, Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
  8. Matteo Novaga, Enrico Valdinoci, Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
  9. Massimiliano Berti, Michela Procesi, Quasi-periodic oscillations for wave equations under periodic forcing
  10. Elena Bosetto, Enrico Serra, Susanna Terracini, Density of chaotic dynamics in periodically forced pendulum-type equations

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