This article is cited in 2 papers

The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions

L. A. Beklaryan

Central Economics and Mathematics Institute, RAS

Abstract: A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation.
Bibliography: 7 titles.

Keywords: functional differential equations, scale of function spaces, impulsive solutions, analogue of Noether's theorem, pointwise completeness of solutions.

UDC: 517.911

MSC: 34K06, 34K10

Received: 04.02.2009 and 20.10.2010

DOI: 10.4213/sm7534

 English version: Sbornik: Mathematics, 2011, 202:3, 307–340

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