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2021•Doklady MathematicsRequires access

The Second Boundary Value Problem for Differential-Difference Equations

А. Л. Скубачевский, Н. О. Иванов

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Abstract

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 $$W_{2}^{1}(0,d)$$ belongs to the space $$W_{2}^{2}(0,d)$$ .

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What this paper is about

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 $$W_{2}^{1}(0,d)$$ belongs to the space $$W_{2}^{2}(0,d)$$ .

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OpenAlex reports 14 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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 $$W_{2}^{1}(0,d)$$ belongs to the space $$W_{2}^{2}(0,d)$$ .

Key concepts: Mathematics, Sobolev space, Mathematical analysis, Boundary value problem, Differential equation, Space (punctuation), Variable (mathematics), Interval (graph theory)

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