E. I. Bravyi

On the Solvability of the Cauchy Problem for Systems of Two Linear Functional Differential Equations

abstract:
The Cauchy problem for a system of two scalar non-Volterra linear functional differential equations is considered. Necessary and sufficient conditions of the solvability are obtained. The method which is used here can be applied to many other boundary value problems for functional differential equations with monotone operators. Some new results on the solvability are announced in the last part of the article.

Mathematics Subject Classification: 34K10, 34K13, 34B05

Key words and phrases: Cauchy problem, boundary value problem, functional differential equation, periodic problem