A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities
Alessio Pomponio - Dipartimento di Matematica, Politecnico di Bari, I–70125 Bari, 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
Received: May 2009; Revised: October 2009; Published: January 2010.
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