Ground State and Geometrically Distinct Solitons of Discrete Nonlinear Schrödinger Equations with Saturable Nonlinearities



We study the discrete nonlinear equation

display math

where math formula (the spectrum of L) and math formula is asymptotically linear as math formula for all math formula. We obtain the existence of ground state solitons and the existence of infinitely many pairs of geometrically distinct solitons of this equation. Our method is based on the generalized Nehari manifold method developed recently by Szulkin and Weth. To the best of our knowledge, this technique has not been used for discrete equations with saturable nonlinearities.