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14 bounded and self-adjoint in the space of all k-periodic sequences. Then a special functional was constructed, the critical points of which in this space are solutions of the original equation. A Gateaux derivative of this functional is found. Next we consider the Nehari manifold for a given variational problem, which is a set of nontrivial critical points of a constructed functional in the space of k-periodic sequences. It is shown that this manifold is a non-empty and closed subset of a given space. In addition, the corresponding minimization problem is considered and it is shown that this problem has a solution in the Nehari manifold. Consequently, under these conditions the original equation has nontrivial periodic solutions. Finally, due to the fact that saturable nonlinearity satisfies these conditions, the existence of two nontrivial standing waves with k-periodic amplitude for a discrete nonlinear Schrödinger equation with saturable nonlinearity on a two-dimensional lattice is established. The results of this paper are the distribution of already known results for discrete nonlinear Schrödinger equations on 1D and 2D-lattices.

matematične ta komp'ûterne modelûvannâ. serìâ: fìziko-matematičnì nauki

Numerical Complex Analysis Method for Parameters Identification of Anisotropic Media Using Applied Quasipotential Tomographic Data. Part 1: Problem Statement and its Approximation