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.
Citation:
L. A. Beklaryan, “The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions”, Sb. Math., 202:3 (2011), 307–340
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\by L.~A.~Beklaryan
\paper The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions
\jour Sb. Math.
\yr 2011
\vol 202
\issue 3
\pages 307--340
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Linking options:
https://www.mathnet.ru/eng/sm7534
https://doi.org/10.1070/SM2011v202n03ABEH004147
https://www.mathnet.ru/eng/sm/v202/i3/p3
This publication is cited in the following 2 articles:
L. A. Beklaryan, A. L. Beklaryan, “Functional differential equations of pointwise type: bifurcation”, Comput. Math. Math. Phys., 60:8 (2020), 1249–1260
Beklaryan L.A., Beklaryan A.L., “Solvability problems for a linear homogeneous functional-differential equation of the pointwise type”, Differ. Equ., 53:2 (2017), 145–156
Citation in format AMSBIB
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