摘要：The aim of this paper is to study the asymptotic stability of positive periodic solution for semilinear evolution equation in an ordered Banach space E: u ′ ( t ) + A u ( t ) = f ( t , u ( t ) ) , t ∈ R + = [ 0 , + ∞ ) , where A : D ( A ) ⊂ E → E is a closed linear operator, and f : R + × E → E is a continuous mapping which is ω-periodic in t. Under order conditions on the nonlinearity f, the asymptotic stability results of positive ω-periodic mild solution are obtained on R + by using operator semigroup theory and a monotone iterative technique. MSC:35B10, 35B40.
