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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.

37L60Lattice dynamics (infinite-dimensional dissipative systems)
34A33Lattice differential equations
58E05Abstract critical point theory
34A35ODE of infinite order
35Q55NLS-like (nonlinear Schrödinger) equations
47J30Variational methods (nonlinear operator equations)
Full Text: DOI
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