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Zbl 1186.35206
Pankov, Alexander; Rothos, Vassilis
Periodic and decaying solutions in discrete nonlinear Schrödinger with saturable nonlinearity. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 464, No. 2100, 3219-3236 (2008). ISSN 1364-5021; ISSN 1471-2946/e

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 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35B10 Periodic solutions of PDE
35B40 Asymptotic behavior of solutions of PDE

Keywords: periodic and decaying solutions; discrete nonlinear Schrödinger; the Nehari manifolds

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