## Existence and concentration of positive solutions for a system of coupled saturable Schrödinger equations.(English)Zbl 1440.35056

Summary: It is considered a saturable system of coupled Schrödinger equations with asymptotically linear nonlinearities. The bound states (solutions with finite energy) are proved to exist and have a concentration behavior under hypotheses involving the coupling and saturation parameters. The proof is based on variational methods.

### MSC:

 35J10 Schrödinger operator, Schrödinger equation 35J47 Second-order elliptic systems 35Q55 NLS equations (nonlinear Schrödinger equations) 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35J20 Variational methods for second-order elliptic equations
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