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Some elements of theory of functional-differrential equation

Annotation

Linear abstract functional-differrential equations are considered. This wide and pithy generalization of classical differrential and functional-differrential equations, impulse systems, singular differrential equations were offered in N.V. Azbelev's, A.V. Anokhin's, L.F. Rakhmatullina's works. Here solvability of boundary value problems is investigated. Representation of Green operator is obtained. Based on investigation of generalized Volterra operator's properties the initial problem is considered. Representation of Cauchy operator is obtained.

Keywords

abstract functional-differrential equation, boundary value problem, Green operator, Cauchy operator, Volterra operator

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Pages

1318-1332

Received

10.04.2009

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