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

Alessio Pomponio; Simone Secchi

doi:10.3934/cpaa.2010.9.741

Article Contents

2010, Volume 9, Issue 3: 741-750. Doi: 10.3934/cpaa.2010.9.741

This issue Previous Article Boundedness and a priori estimates of solutions to elliptic systems with Dirichlet-Neumann boundary conditions Next Article Estimates for extremal values of $-\Delta u= h(x) u^{q}+\lambda W(x) u^{p}$

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

Alessio Pomponio^1, and
Simone Secchi^2,

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

Received: April 30, 2009

Revised: September 30, 2009

Published: April 2010

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Abstract

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.

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

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