Geodesic
Smoothness of generalized solutions of a boundary-value problem for a second-order differential-difference equation with mixed boundary conditions
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 3, pp. 399-417

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We consider a boundary-value problem with mixed boundary conditions for a second-order differential-difference equation on a finite interval $(0,d).$ We prove existence of a generalized solution of the problem and study the conditions on the right-hand side of the differential-difference equation ensuring the smoothness of the generalized solution over the entire interval.
Keywords: boundary-value problem, differential-difference equations, generalized solutions. 
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     title = {Smoothness of generalized solutions of a boundary-value problem for a second-order differential-difference equation with mixed boundary conditions},
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N. O. Ivanov. Smoothness of generalized solutions of a boundary-value problem for a second-order differential-difference equation with mixed boundary conditions. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 3, pp. 399-417. http://geodesic.mathdoc.fr/item/CMFD_2023_69_3_a1/