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