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Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity. (English) Zbl 1186.35206
Summary: We demonstrate the existence of solutions in the discrete nonlinear Schrödinger equation (DNLS) with saturable nonlinearity. We consider two types of solutions to DNLS periodic and vanishing at infinity. Calculus of variations and the Nehari manifolds are employed to establish the existence of these solutions. We present some extensions of our results, combining the Nehari manifold approach and the Mountain Pass argument.
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35B10Periodic solutions of PDE
35B40Asymptotic behavior of solutions of PDE