Geodesic
The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation
Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 295-302

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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. 
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     author = {B. I. Efendiev},
     title = {The {Dirichlet} {Problem} for an {Ordinary} {Continuous} {Second-Order} {Differential} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {295--302},
     publisher = {mathdoc},
     volume = {103},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a10/}
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B. I. Efendiev. The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation. Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 295-302. http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a10/