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functional differential equation; functional nondifferential equation; asymptotic behaviour; transformation
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 \[\sum _{i=1}^m|a_i(x)|\omega (\tau _i(x))+b(x)\omega (x)=0.\]
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