On linearly coupled Schrödinger systems

Chen, Zhijie; Zou, Wenming

doi:10.1090/S0002-9939-2013-12000-9

On linearly coupled Schrödinger systems
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by Zhijie Chen and Wenming Zou PDF

Proc. Amer. Math. Soc. 142 (2014), 323-333 Request permission

Abstract:

We study the following system of nonlinear Schrödinger equations: \[ \begin {cases} -\Delta u +u = f(u)+\lambda v, & x\in \mathbb {R}^N,\\ -\Delta v +v = g(v)+\lambda u, & x\in \mathbb {R}^N. \end {cases} \] Under almost optimal assumptions on $f$ and $g$, for small $\lambda >0$, we obtain positive radial solutions and study their asymptotic behaviors as $\lambda \to 0$.

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