×

Multiple periodic solutions for two-dimensional lattice dynamic systems. (English) Zbl 1107.34036

The authors establish existence results for infinitely many periodic motions for a two-dimensional lattice of \(M\times N\) particles with nearest-neighbor interaction.

MSC:

34C25 Periodic solutions to ordinary differential equations
34A35 Ordinary differential equations of infinite order
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Arioli, G.; Gazzola, F., Periodic motions of an infinite lattice of particles with nearest neighbor interaction, Nonlinear anal., 26, 6, 1103-1114, (1996) · Zbl 0867.70004
[2] Arioli, G.; Gazzola, F., Existence and numerical approximation of periodic motions of an infinite lattice of particles, Z. angew. math. phys., 46, 6, 898-912, (1995) · Zbl 0838.34046
[3] Arioli, G.; Gazzola, F.; Terracini, S., Multibump periodic motions of an infinite lattice of particles, Math. Z., 223, 4, 627-642, (1996) · Zbl 0871.34028
[4] Rabinowitz, P.H., On large norm periodic solutions of some differential equations, (), 193-210
[5] Ruf, B.; Srikanth, P.N., On periodic motions of lattices of Toda type via critical point theory, Arch. ration. mech. anal., 126, 4, 369-385, (1994) · Zbl 0809.34056
[6] Srikanth, P.N., On periodic motions of two-dimensional lattices, (), 118-122 · Zbl 0892.34041
[7] Toda, M., Theory of nonlinear lattices (M. Toda, trans.), (), (from Japanese)
[8] Torres, P.J., Necessary and sufficient conditions for existence of periodic motions of forced systems of particles, Z. angew. math. phys., 52, 3, 535-540, (2001) · Zbl 1001.34038
[9] Torres, P.J., Periodic motions of forced infinite lattices with nearest neighbor interaction, Z. angew. math. phys., 51, 3, 333-345, (2000) · Zbl 0999.82050
[10] Torres, P.J., Periodic motions of non-autonomous Toda lattices, (), 434-436 · Zbl 0969.34037
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.