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

Pages: 741 - 750, Volume 9, Issue 3, May 2010

doi:10.3934/cpaa.2010.9.741       Abstract        Full Text (175.0K)       Related Articles

Alessio Pomponio - Dipartimento di Matematica, Politecnico di Bari, I–70125 Bari, Italy (email)
Simone Secchi - Dipartimento di Matematica ed Applicazioni, Università di Milano–Bicocca, I–20125 Milano, Italy (email)

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.

Keywords:  Nonlinear Schrödinger systems, Nehari manifold, ground-state solutions.
Mathematics Subject Classification:  Primary: 35J50, 35Q55; Secondary: 58E05.

Received: May 2009;      Revised: October 2009;      Published: January 2010.