Homoclinics : Poincaré-Melnikov type results via a variational approach
Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 2, p. 233-252
@article{AIHPC_1998__15_2_233_0,
     author = {Ambrosetti, Antonio and Badiale, Marino},
     title = {Homoclinics : Poincar\'e-Melnikov type results via a variational approach},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {2},
     year = {1998},
     pages = {233-252},
     zbl = {1004.37043},
     mrnumber = {1614571},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1998__15_2_233_0}
}
Ambrosetti, Antonio; Badiale, Marino. Homoclinics : Poincaré-Melnikov type results via a variational approach. Annales de l'I.H.P. Analyse non linéaire, Volume 15 (1998) no. 2, pp. 233-252. http://www.numdam.org/item/AIHPC_1998__15_2_233_0/

[1] A. Ambrosetti, Critical points and nonlinear variational problems. Supplément au Bull. Soc. Math. de France, Vol. 120, 1992. | Numdam | MR 1164129 | Zbl 0766.49006

[2] A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of Nonlinear Schrödinger equations, Archive Rat. Mech. Analysis, to appear. | Zbl 0896.35042

[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. | Numdam | MR 1229052 | Zbl 0806.58018

[4] A. Ambrosetti, V. Coti Zelati and I. Ekeland, Symmetry breaking in Hamiltonian systems, Jour. Diff. Equat., Vol. 67, 1987, pp. 165-184. | MR 879691 | Zbl 0606.58043

[5] F.A. Berezin and M.A. Shubin, The Schrödinger Equation. Kluwer Acad. Publ., Dordrecht, 1991. | MR 1186643 | Zbl 0749.35001

[6] U. Bessi, A variational proof of a Sitnikov-like theorem, Nonlin. Anal. TMA, Vol. 20, 1993, pp. 1303-1318. | MR 1220837 | Zbl 0778.34036

[7] S.V. Bolotin, Homoclinic orbits to invariant tori of Hamiltonian systems, A.M.S. Transl., Vol. 168, 1995, pp. 21-90. | Zbl 0847.58024

[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. | MR 1070929 | Zbl 0731.34050

[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. | MR 1119200 | Zbl 0744.34045

[10] V.V. Kozlov, Integrability and non-integrability in Hamiltonian Mechanics. Russian Math. Surveys, Vol. 38, 1983, pp. 1-76. | Zbl 0525.70023

[11] U. Kirchgraber and D. Stoffer, Chaotic behaviour in simple dynamical systems, SIAM Review, Vol. 32, 1990, pp. 424-452. | MR 1069896 | Zbl 0715.58024

[12] L. Jeanjean, Two positive solutions for a class of nonhomogeneous elliptic equations, preprint. | MR 1741765

[13] S. Mathlouti, Bifurcation d'horbites homoclines pour les systèmes hamiltoniens. Ann. Fac. Sciences Toulouse, Vol. 1, 1992, pp. 211-235. | Numdam | Zbl 0780.58034

[14] V.K. Melnikov, On the stability of the center for time periodic perturbations, Trans. Moscow Math. Soc., Vol. 12, 1963, pp. 3-52. | MR 156048 | Zbl 0135.31001

[15] H. Poincaré, Les Méthodes nouvelles de la méchanique céleste., 1892.

[16] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z., Vol. 209, 1992, pp. 27-42. | MR 1143210 | Zbl 0725.58017

[17] E. Séré, Looking for the Bernoulli Shift, Ann. Inst. H. Poincaré, Anal. nonlin., Vol. 10, 1993, pp. 561-590. | Numdam | MR 1249107 | Zbl 0803.58013

[18] K. Tanaka, A note on the existence of multiple homoclinics orbits for a perturbed radial potential, NoDEA, Vol. 1, 1994, pp. 149-162. | MR 1273347 | Zbl 0819.34032