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

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  • 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.

    Mathematics Subject Classification: Primary: 35J50, 35Q55; Secondary: 58E05.

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