Geodesic
The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions
Sbornik. Mathematics, Tome 202 (2011) no. 3, pp. 307-340

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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, analogue of Noether's theorem, pointwise completeness of solutions.
Mots-clés : impulsive solutions 
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     title = {The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions},
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L. A. Beklaryan. The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions. Sbornik. Mathematics, Tome 202 (2011) no. 3, pp. 307-340. http://geodesic.mathdoc.fr/item/SM_2011_202_3_a0/