Asymptotic and integral equivalence of functional and ordinary differential equations. (English) Zbl 0729.34059

Morchało, Jarosław

Arch. Math., Brno 26, No. 1, 37-47 (1990).

The author considers the following two systems: \((1)\quad u'(t)=A(t)u(t)+F(t,u_ t),\) \((2)\quad v'(t)=A(t)v(t).\) He proves that under certain conditions upon system (2) and the nonlinear term F, there exists a homeomorphism between the sets of g-bounded solutions of (1) and (2), respectively.

Reviewer: M.Lizana (Caracas)

MSC:

34K25	Asymptotic theory of functional-differential equations
34K05	General theory of functional-differential equations

Keywords:

functional differential equations; asymptotic equivalence; homeomorphism; g-bounded solutions