MATHEMATICA BOHEMICA, Vol. 133, No. 4, pp. 435-445, 2008

General conditions guaranteeing the solvability of the Cauchy problem for
functional differential equations

N. Dilna, A. Ronto

N. Dilna, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska St., 016 01 Kiev, Ukraine, e-mail: dilna@imath.kiev.ua, current address: Mathematical Institute of the Slovak Academy of Sciences, Stefanikova 49, 814 73 Bratislava, Slovak Republic; A. Ronto, Institute of Mathematics, Academy of Sciences of Czech Republic, Zizkova 22, CZ-616 62 Brno, Czech Republic, e-mail: ronto@ipm.cz

Abstract: New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.

Keywords: functional differential equation, Cauchy problem, initial value problem, differential inequality

Classification (MSC 2000): 34K06, 34K10

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