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The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation

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Abstract

The extremum principle for an ordinary continuous second-order differential equation with variable coefficients is proved and this principle is used to establish the uniqueness of the solution of the Dirichlet problem. The problem under consideration is equivalently reduced to the Fredholm integral equation of the second kind and the unique solvability of this integral equation is proved.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Nalchik, Russia

    B. I. Éfendiev

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  1. B. I. Éfendiev
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Correspondence to B. I. Éfendiev.

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Original Russian Text © B. I. Éfendiev, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 2, pp. 295–302.

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Éfendiev, B.I. The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation. Math Notes 103, 290–296 (2018). https://doi.org/10.1134/S0001434618010297

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