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May  2010, 9(3): 741-750. doi: 10.3934/cpaa.2010.9.741

## A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities

 1 Dipartimento di Matematica, Politecnico di Bari, I–70125 Bari, Italy 2 Dipartimento di Matematica ed Applicazioni, Università di Milano–Bicocca, I–20125 Milano, Italy

Received  May 2009 Revised  October 2009 Published  January 2010

We prove the existence of radially symmetric ground--states for the system of Nonlinear Schrödinger equations

$-\Delta u+ u=f(u)+\beta u v^2$ in $R^3,$

$-\Delta v+ v=g(v)+\beta u^2 v$ in $R^3,$

under very weak assumptions on the two nonlinearities $f$ and $g$. In particular, no "Ambrosetti--Rabinowitz" condition is required.

Citation: Alessio Pomponio, Simone Secchi. A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities. Communications on Pure and Applied Analysis, 2010, 9 (3) : 741-750. doi: 10.3934/cpaa.2010.9.741
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