Uniqueness of positive bound states to Schrodinger systems with critical exponents

Congming Li; Li Ma

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arXiv · 0708.0286

Uniqueness of positive bound states to Schrodinger systems with critical exponents

Congming Li·Li Ma

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Abstract

We prove the uniqueness for the positive solutions of the following elliptic systems: \begin{eqnarray*} \left\{\begin{array}{ll} - \lap (u(x)) = u(x)^αv(x)^β - \lap (v(x)) = u(x)^β v(x)^α \end{array} \right. \end{eqnarray*} Here $x\in R^n$, $n\geq 3$, and $1\leq α, β\leq \frac{n+2}{n-2}$ with $α+β=\frac{n+2}{n-2}$. In the special case when $n=3$ and $α=2, β=3$, the systems come from the stationary Schrodinger system with critical exponents for Bose-Einstein condensate. As a key step, we prove the radial symmetry of the positive solutions to the elliptic system above with critical exponents.

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BibTeX RIS

Congming Li, Li Ma. 2007-08-02. Uniqueness of positive bound states to Schrodinger systems with critical exponents. https://arxiv.org/abs/0708.0286

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