Éfendiev, B. I. The Dirichlet problem for an ordinary continuous second-order differential equation. (English. Russian original) Zbl 1394.34009 Math. Notes 103, No. 2, 290-296 (2018); translation from Mat. Zametki 103, No. 2, 295-302 (2018). Summary: 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. MSC: 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 45B05 Fredholm integral equations Keywords:continuous differential equation; fractional integro-differential operator; Dirichlet problem; extremum principle × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Nakhushev, A. M., Continuous differential equations and their difference analogues, Dokl. Akad. Nauk SSSR, 300, 796-799, (1988) · Zbl 0684.34015 [2] Nakhushev, A. M., On the positivity of continuous and discrete differentiation and integration operators that are very important in fractional calculus and in the theory of equations of mixed type, Differ. Uravn., 34, 101-109, (1998) · Zbl 0948.26004 [3] Pskhu, A. V., On the theory of the continual integro-differentiation operator, Differ. Uravn., 40, 120-127, (2004) · Zbl 1082.45010 [4] A. M. Nakhushev, Fractional Calculus and Its Application (Fizmatlit, Moscow, 2003) [in Russian]. · Zbl 1066.26005 [5] A. V. Pskhu, Partial Differential Equations of Fractional Order (Nauka, Moscow, 2005) [in Russian]. · Zbl 1193.35245 [6] Nakhushev, A. M., The Sturm-Liouville problem for an ordinary second-order differential equation with fractional derivatives in the lowest terms, Dokl. Akad. Nauk SSSR, 234, 308-311, (1977) · Zbl 0376.34015 [7] Gadzova, L. Kh., On the theory of boundary-value problems for a differential equation of fractional order with constant coefficients, Dokl. Adygeisk. (Cherkessk.) Mezhdunar. Akad. Nauk, 16, 34-40, (2014) · Zbl 1296.34019 [8] Gadzova, L. Kh., Generalized Dirichlet problem for a fractional linear differential equation with constant coefficients, Differ. Uravn., 50, 121-125, (2014) · Zbl 1296.34019 [9] Éfendiev, B. I., Cauchy problemfor a second-order ordinary differential equation with a continual derivative, Differ. Uravn., 47, 1364-1368, (2011) · Zbl 1235.34013 [10] Éfendiev, B. I., Steklov problemfor a second-order ordinary differential equation with a continual derivative, Differ. Uravn., 49, 469-475, (2013) · Zbl 1273.34006 [11] Éfendiev, B. I., Dirichlet problem for second-order ordinary differential equations with segment-order derivative, Mat. Zametki, 97, 620-628, (2015) · Zbl 1329.34006 · doi:10.4213/mzm8789 [12] Éfendiev, B. I., Initial-value problem for a continuous second-order differential equation, Differ. Uravn., 50, 564-568, (2014) · Zbl 1304.34017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.