Geodesic
Asymptotic estimation for functional differential equations with several delays
Archivum mathematicum, Tome 35 (1999) no. 4, pp. 337-345 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We discuss the asymptotic behaviour of all solutions of the functional differential equation \[y^{\prime }(x)=\sum _{i=1}^ma_i(x)y(\tau _i(x))+b(x)y(x)\,,\] where $b(x)0$. The asymptotic bounds are given in terms of a solution of the functional nondifferential equation \[\sum _{i=1}^m|a_i(x)|\omega (\tau _i(x))+b(x)\omega (x)=0.\]
We discuss the asymptotic behaviour of all solutions of the functional differential equation \[y^{\prime }(x)=\sum _{i=1}^ma_i(x)y(\tau _i(x))+b(x)y(x)\,,\] where $b(x)0$. The asymptotic bounds are given in terms of a solution of the functional nondifferential equation \[\sum _{i=1}^m|a_i(x)|\omega (\tau _i(x))+b(x)\omega (x)=0.\]
Classification : 34K25, 39B99
Keywords: functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation 
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Čermák, Jan. Asymptotic estimation for functional differential equations with several delays. Archivum mathematicum, Tome 35 (1999) no. 4, pp. 337-345. http://geodesic.mathdoc.fr/item/ARM_1999_35_4_a5/

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