Standing wave solutions for the discrete coupled nonlinear Schrödinger equations with unbounded potentials. (English) Zbl 1291.34146
Summary: We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero.
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 34A33 | Ordinary lattice differential equations |
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