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arXiv · 0912.0150

Existence and bounds of positive solutions for a nonlinear Schroedinger system

Benedetta Noris·Miguel Ramos
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Abstract

We prove that, for any real $λ$, the system $-Δu +λu = u^3-βuv^2$, $ -Δv+λv =v^3-βvu^2$, $ u,v\in H^1_0(Ω),$ where $Ω$ is a bounded smooth domain of $R^3$, admits a bounded family of positive solutions $(u_β, v_β)$ as $β\to +\infty$. An upper bound on the number of nodal sets of the weak limits of difference $u_β-v_β$ is also provided. Moreover, for any sufficiently large fixed value of $β>0$ the system admits infinitely many positive solutions.

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Benedetta Noris, Miguel Ramos. 2009-12-01. Existence and bounds of positive solutions for a nonlinear Schroedinger system. https://arxiv.org/abs/0912.0150

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