On the monotonicity property of the generalized eigenvalue for weakly-coupled cooperative elliptic systems

We consider general linear non-degenerate weak-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in Rd with respect to potential. It is shown that on right equivalent recurrence property twisted operator which is, turn, minimal growth at infinity eigenfunctions. The strict be exponential stability operators. An equivalence between stochastic representation eigenfunction also established.