Positive Solutions of Advanced Differential Systems

Abstract EN

We study asymptotic behavior of solutions of general advanced differential systems y˙(t)=F(t,yt), where F:Ω→ℝn is a continuous quasi-bounded functional which satisfies a local Lipschitzcondition with respect to the second argument and Ω is a subset in ℝ×Crn, Crn:=C([0,r],ℝn),yt∈Crn, and yt(θ)=y(t+θ), θ∈[0,r].

A monotone iterative method is proposed to provethe existence of a solution defined for t→∞ with the graph coordinates lying betweengraph coordinates of two (lower and upper) auxiliary vector functions.

This result is applied to scalar advanced linear differential equations.

Criteria of existence of positive solutions are given and their asymptotic behavior is discussed.