ft'e study the global existence, the atabnity mzd the asympt:otic behavior oj" solutions of the j"wzctional Jijferential equations x ' ( t) = a ( t) x (r {t)) + b:r;( t), h r; JJi r,;here r i.s a continuous contraci;Íon al infinity. l. INTROOUCTION We study the asymptotic behavior of the solutions of the functional differential equation : x'(t) = a(t) x (r(t)} + bx(t) b G IR ( 1.1) where a [0,=) + [O,oo) and r : [O,oo) + [O,m) are continuous functions. Particular cases of this equation have

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... studied by a number of authors. BELLMAN-COOKE [1], DRIVER [4] and HALE [8] are excellents references for knowing its history. The work of DE BRUIJN [2,3] treats several particular cases. KRASOVSKI [12] studied the case r(t) = t-1(t), O,:. 1 (t) f. 1 0 . KATO-Mc LEOD [10, 11, 15] and MAHLER [14] considered