论文标题
关于弱耦合合作椭圆系统的广义特征值的单调性能
On the monotonicity property of the generalized eigenvalue for weakly-coupled cooperative elliptic systems
论文作者
论文摘要
我们考虑一般的线性非脱位弱耦合的椭圆系统，并研究了$ \ Mathbb {r}^d $在潜在的$ \ mathbb {r}^d中的某些单调性能。结果表明，右侧的单调性等于扭曲操作员的复发性质，这反过来又等同于主要特征函数无穷大的最小生长特性。主要特征值的严格单调性能与扭曲操作员的指数稳定性相同。还建立了右侧的单调性能与主征函数的随机表示之间的等效性。
We consider general linear non-degenerate weakly-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in $\mathbb{R}^d$ with respect to the potential. It is shown that monotonicity on the right is equivalent to the recurrence property of the twisted operator which is, in turn, equivalent to the minimal growth property at infinity of the principal eigenfunctions. The strict monotonicity property of the principal eigenvalue is shown to be equivalent with the exponential stability of the twisted operators. An equivalence between the monotonicity property on the right and the stochastic representation of the principal eigenfunction is also established.
