×

Multibump periodic motions of an infinite lattice of particles. (English) Zbl 0871.34028

We prove the existence of infinitely many periodic motions of an infinite lattice of particles with repulsive-attractive nearest neighbor interaction. Under a suitable assumption we prove that these solutions are of multibump type by a construction procedure.

MSC:

37-XX Dynamical systems and ergodic theory
70F35 Collision of rigid or pseudo-rigid bodies
70K50 Bifurcations and instability for nonlinear problems in mechanics
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal.14 (1973) 349–381 · Zbl 0273.49063
[2] G. Arioli, F. Gazzola, Periodic motions of an infinite lattice of particles with nearest neighbor interaction, Nonl. Anal. TMA26 6) (1996) 1103–1114 · Zbl 0867.70004
[3] G. Arioli, F. Gazzola, Existence and numerical approximation of periodic motions of an infinite lattice of particles, Z.A.M.P.46 (1995) 898–912 · Zbl 0838.34046
[4] P. Caldiroli, P. Montecchiari, Homoclinic orbits for second order Hamiltonian systems with potential changing sign, Comm. Appl. Nonl. Anal.1 (1994) 97–129 · Zbl 0867.70012
[5] V. Coti Zelati, I. Ekeland, E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann.288 (1990) 133–160 · Zbl 0731.34050
[6] V. Coti Zelati, P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. of the AMS4, 4 (1991) 693–727 · Zbl 0744.34045
[7] V. Coti Zelati, P.H. Rabinowitz, Homoclinic type solutions for a semilinear elliptic PDE on \(\mathbb{R}\) n , Comm. Pure App. Math.XLV (1992) 1217–1269 · Zbl 0785.35029
[8] J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems Applied Math. Sciences74, New York, Springer-Verlag, 1989 · Zbl 0676.58017
[9] C. Miranda, Un’osservazione su un teorema di Brouwer, Boll. Un. Mat. It.II, III (1940–1941) 5–7
[10] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z.209, (1992) 27–42 · Zbl 0739.58023
[11] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H.P.10, 5 (1993) 561–590
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.