Geodesic
The second boundary value problem for differential-difference equations
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 74-77.

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We consider the second boundary value problem for a second-order differential-difference equation with variable coefficients on the interval $(0,d)$. It was obtained the necessary and sufficient condition for the existence of a generalized solution. It was proved that, if the right-hand side of the equation is orthogonal in $L_2(0,d)$ to some functions, then a generalized solution from the Sobolev space $W^1_2(0,d)$ belongs to the space $W_2^2(0,d)$.
Keywords: differential–difference equations, generalized solutions, boundary value problem. 
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A. L. Skubachevskii; N. O. Ivanov. The second boundary value problem for differential-difference equations. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 74-77. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a13/

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