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Existence of breather solutions of the DNLS equations with unbounded potentials. (English) Zbl 1238.37030

Summary: We use a discrete version of the compact embedding theorem and the Nehari manifold approach to show the existence of nontrivial breather solutions without the Palais-Smale condition.

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
34A33 Ordinary lattice differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
34A35 Ordinary differential equations of infinite order
35Q55 NLS equations (nonlinear Schrödinger equations)
47J30 Variational methods involving nonlinear operators
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