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Breather solutions of the discrete nonlinear Schrödinger equations with unbounded potentials. (English) Zbl 1200.37072

Summary: In this paper the author investigates the existence of nontrivial breather solutions of the discrete nonlinear Schrödinger equation with the unbounded potential at infinity. First he derives a discrete version of compact embedding theorem. Then combining the Nehari manifold approach and the compact embedding theorem, he shows the existence of breather solutions without Palais-Smale condition. The results on the exponential decay of breather solutions are also provided in this paper.

Editorial remark: No review copy delivered.

MSC:
37K60Lattice dynamics (infinite-dimensional systems)
37K40Soliton theory, asymptotic behavior of solutions