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Mat. Zametki, 2018, Volume 103, Issue 2, Pages 295–302 (Mi mz11010)  

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

B. I. Efendiev

Institute of Applied Mathematics and Automation, Nalchik

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.

Keywords: continuous differential equation, fractional integro-differential operator, Dirichlet problem, extremum principle.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00462
This work was supported by the Russian Foundation for Basic Research under grant 16-01-00462.


DOI: https://doi.org/10.4213/mzm11010

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English version:
Mathematical Notes, 2018, 103:2, 290–296

Bibliographic databases:

UDC: 517.927.2
Received: 10.11.2015

Citation: B. I. Efendiev, “The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation”, Mat. Zametki, 103:2 (2018), 295–302; Math. Notes, 103:2 (2018), 290–296

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