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
Access Full Article
topHow to cite
topAmbrosetti, 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
top- [1] A. Ambrosetti, Critical points and nonlinear variational problems. Supplément au Bull. Soc. Math. de France, Vol. 120, 1992. Zbl0766.49006MR1164129
- [2] A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of Nonlinear Schrödinger equations, Archive Rat. Mech. Analysis, to appear. Zbl0896.35042
- [3] A. Ambrosetti and V. Coti Zelati, Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova, Vol. 89, 1993, pp. 177-194, and Note C.R.A.S., Vol. 314, 1992, pp. 601-604. Zbl0806.58018MR1229052
- [4] A. Ambrosetti, V. Coti Zelati and I. Ekeland, Symmetry breaking in Hamiltonian systems, Jour. Diff. Equat., Vol. 67, 1987, pp. 165-184. Zbl0606.58043MR879691
- [5] F.A. Berezin and M.A. Shubin, The Schrödinger Equation. Kluwer Acad. Publ., Dordrecht, 1991. Zbl0749.35001MR1186643
- [6] U. Bessi, A variational proof of a Sitnikov-like theorem, Nonlin. Anal. TMA, Vol. 20, 1993, pp. 1303-1318. Zbl0778.34036MR1220837
- [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] 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] 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] V.V. Kozlov, Integrability and non-integrability in Hamiltonian Mechanics. Russian Math. Surveys, Vol. 38, 1983, pp. 1-76. Zbl0525.70023
- [11] U. Kirchgraber and D. Stoffer, Chaotic behaviour in simple dynamical systems, SIAM Review, Vol. 32, 1990, pp. 424-452. Zbl0715.58024MR1069896
- [12] L. Jeanjean, Two positive solutions for a class of nonhomogeneous elliptic equations, preprint. Zbl0890.35048MR1741765
- [13] S. Mathlouti, Bifurcation d'horbites homoclines pour les systèmes hamiltoniens. Ann. Fac. Sciences Toulouse, Vol. 1, 1992, pp. 211-235. Zbl0780.58034
- [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] H. Poincaré, Les Méthodes nouvelles de la méchanique céleste., 1892. Zbl25.1847.03
- [16] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., Vol. 209, 1992, pp. 27-42. Zbl0725.58017MR1143210
- [17] E. Séré, Looking for the Bernoulli Shift, Ann. Inst. H. Poincaré, Anal. nonlin., Vol. 10, 1993, pp. 561-590. Zbl0803.58013MR1249107
- [18] K. Tanaka, A note on the existence of multiple homoclinics orbits for a perturbed radial potential, NoDEA, Vol. 1, 1994, pp. 149-162. Zbl0819.34032MR1273347
Citations in EuDML Documents
top- A. Ambrosetti, D. Arcoya, J. L. Gámez, Asymmetric bound states of differential equations in nonlinear optics
- Matthias Schneider, Prescribing scalar curvature on
- Andrea Malchiodi, Some existence results for the scalar curvature problem via Morse theory
- 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
- Marta Macrì, Soluzioni omocline a varietà invarianti: un approccio variazionale
- Antonio Ambrosetti, Veronica Felli, Andrea Malchiodi, Ground States of Nonlinear Schrödinger Equations with potentials vanishing at infinity
- Matteo Novaga, Enrico Valdinoci, Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
- Massimiliano Berti, Michela Procesi, Quasi-periodic oscillations for wave equations under periodic forcing
- Matteo Novaga, Enrico Valdinoci, Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations
- Elena Bosetto, Enrico Serra, Susanna Terracini, Density of chaotic dynamics in periodically forced pendulum-type equations
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.