Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 1, p. 107-135
@article{AIHPC_1999__16_1_107_0,
     author = {Alessio, Francesca and Montecchiari, Piero},
     title = {Multibump solutions for a class of lagrangian systems slowly oscillating at infinity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {1},
     year = {1999},
     pages = {107-135},
     zbl = {0919.34044},
     mrnumber = {1668564},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_1_107_0}
}
Alessio, Francesca; Montecchiari, Piero. Multibump solutions for a class of lagrangian systems slowly oscillating at infinity. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 1, pp. 107-135. http://www.numdam.org/item/AIHPC_1999__16_1_107_0/

[1] F. Alessio, Homoclinic solutions for second order systems with expansive time dependence, preprint, 1996. | MR 1463919

[2] A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of nonlinear Schrödinger equation, Arch. Rat. Mech. Anal., to appear. | Zbl 0896.35042

[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. | MR 1190931 | Zbl 0804.34046

[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. | Numdam | MR 1229052 | Zbl 0806.58018

[5] U. Bessi, A Variational Proof of a Sitnikov-like Theorem, Nonlinear Anal. TMA, Vol. 20, 1993, pp. 1303-1318. | MR 1220837 | Zbl 0778.34036

[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. | MR 1355162 | Zbl 0858.34039

[7] S. Bolotin, Existence of homoclinic motions, Vestnik Moskov. Univ. Ser. I Mat. MeKh., Vol.6, 1980, pp. 98-103. | MR 728558 | Zbl 0549.58019

[8] B. Buffoni and E. Séré, A global condition for quasi random behaviour in a class of conservative systems, preprint, 1995. | MR 1374173

[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. | MR 1280118 | Zbl 0867.70012

[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. | MR 1414014 | Zbl 0951.37013

[11] K. Cieliebak and E. Séré, Pseudo-holomorphic curves and the shadowing Lemma, Duke Math. Journ., to appear. | Zbl 0955.37039

[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. | MR 1070929 | Zbl 0731.34050

[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. | Zbl 0878.34045

[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. | MR 1119200 | Zbl 0744.34045

[15] M. Del Pino and P.L. Felmer, Multipeak bound states for nonlinear Schrödinger equations, Ann. IHP Anal. Nonlinéaire, to appear. | Numdam | MR 1614646 | Zbl 0901.35023

[16] C. Gui, Existence of multi-bump solutions for nonlinear Schrödinger equations via variational methods, Comm. in PDE, Vol. 21, 1996, pp. 787-820. | MR 1391524 | Zbl 0857.35116

[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. | MR 1079873 | Zbl 0702.34039

[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. | Numdam | MR 778970 | Zbl 0541.49009

[19] C. Miranda, Un'osservazione su un teorema di Brouwer, Boll. Unione Mat. Ital., Vol. 3, 1940, pp. 5-7. | MR 4775 | Zbl 0024.02203

[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. | MR 1378249 | Zbl 0849.34035

[21] P. Montecchiari, M. Nolasco and S. Terracini, Multiplicity of homoclinics for time recurrent second order systems, Calculus of Variations, to appear. | Zbl 0886.58014

[22] P. Montecchiari, M. Nolasco and S. Terracini, A global condition for periodic Duffing-like equations, preprint, SISSA, 1995. | MR 1487629 | Zbl 0926.37005

[23] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh, Vol. 114 A, 1990, pp. 33-38. | MR 1051605 | Zbl 0705.34054

[24] P.H. Rabinowitz, Multibump solutions for an almost periodically forced singular Hamiltonian system, preprint, 1995. | MR 1348521 | Zbl 0828.34034

[25] P.H. Rabinowitz, A multibump construction in a degenerate setting, preprint, 1996. | MR 1433175 | Zbl 0876.34055

[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. | MR 1095767 | Zbl 0707.58022

[27] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit., Vol. 209, 1991, pp. 27-42. | MR 1143210 | Zbl 0725.58017

[28] E. Séré, Looking for the Bernoulli shift, Ann. IHP Anal. Nonlinéaire, Vol. 10, 1993, pp. 561-590. | Numdam | MR 1249107 | Zbl 0803.58013

[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. | Numdam | MR 1420498 | Zbl 0873.58032

[30] S. Wiggins, Global bifurcation and chaos, Applied Mathematical Sciences, Springer-Verlag, Vol. 73,1988. | Zbl 0661.58001