Positive Solutions of Advanced Differential Systems
Keyword(s):
We study asymptotic behavior of solutions of general advanced differential systemsy˙(t)=F(t,yt), whereF:Ω→ℝnis a continuous quasi-bounded functional which satisfies a local Lipschitz condition with respect to the second argument andΩis a subset inℝ×Crn,Crn:=C([0,r],ℝn),yt∈Crn, andyt(θ)=y(t+θ),θ∈[0,r]. A monotone iterative method is proposed to prove the existence of a solution defined fort→∞with the graph coordinates lying between graph 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.
2018 ◽
Vol 26
(1)
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pp. 5-41
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1998 ◽
Vol 144
(2)
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pp. 321-352
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1963 ◽
Vol 14
(1)
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pp. 12-12
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