Literature Cited
E. S. Chichkin, “A Theorem on a Differential Inequality for Multipoint Boundary Value Problems.” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No 2, pp. 170–179, [in Russian] (1962).
N. V. Azbelev, A. Ya. Khokhryakov, and Z. B. Tsalyuk, “Theorems on a Differential Inequality for Boundary Value Problems.” Matem. Sb.,59, No. 1, pp. 125–144, [in Russian] (1962).
R. G. Aliev, “Multipoint Boundary Value Problem for an Ordinary Fourth-Order Differential Equation.” Avtoreferat Kandidatskoi Dissertatsii, Kazansk. Un-t, [in Russian] (1963).
I. N. Inozemtseva, “A Theorem on the Sign of the Green's Function for a Linear Fifth-Order Differential Equation.” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 1, pp. 68–72 (1965).
Ch. J. de la Vallée-Poussin, Sur l'Équation Differentielle du Second Ordre. Détermination d'une Intégrale par Deux Valeurs Assignées. Extension aux Équations d'Ordre n, J. Math. pures et appl.,8, 125–144 (1929).
G. Sansone, Ordinary Differential Equations, Vol. 1, IL, Moscow, [Russian translation from the Italian] (1958).
A. Yu. Levin, “A Multipoint Boundary Value Problem.” Nauchn. Doklady Vysshei Shkoly, Fiz.-Matem. Nauki, No. 5, pp. 34–37, [in Russian] (1958).
A. Yu. Levin, “Certain Estimates of a Differentiable Function.” Doklady Akad. Nauk SSSR,138 No. 1, pp. 37–38, [in Russian] (1961).
A. Yu. Levin, “An Estimate for a Function with Monotonically Distributed Zeros of Successive Derivatives.” Matem. Sb.,64, No. 3, pp. 396–409, [in Russian] (1964).
G. A. Bessmertnykh and A. Yu. Levin, “Some Estimates for Differentiable Functions of a Single Variable.” Doklady Akad. Nauk SSSR,144, No. 3, pp. 471–474, [in Russian] (1962).
A. L. Teptin, “The Behavior of the Green's Function of a Multipoint Linear Difference Boundary Value Problem.” ibid.,147, No. 1, pp. 38–40, [in Russian] (1962).
A. L. Teptin, “Theorems on Difference Inequalities for n-Point Difference Boundary Value Problems.” Matem. Sb.,62, No. 3, pp. 345–370 (1963).
N. Ya. Vilenkin, E. A. Gorin, A. G. Kostyuchenko, et al., Functional Analysis. S. G. Krein (Editor), Izd. “Nauka,” Moscow, [in Russian] (1964).
A. L. Teptin, “Conditions for the Solvability of the Chaplygin Problem for Linear Difference Equations.” Izv. Vyssh. Uchebn. Zavedenii, Matematika, No. 4, pp. 265–269, [in Russian] (1958).
A. L. Teptin, “Conditions for the Solvability of the Chaplygin Problem for Difference Equations.” Kandidatskaya Dissertatsiya, Kazansk. Un-t., [in Russian] (1962).
A. O. Gel'fond, Calculus of Finite Differences, Fizmatgiz, Moscow, [in Russian] (1959).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 6, pp. 1370–1382, November–December, 1966.
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Teptin, A.L. Estimate of the interval of nonoscillation for a finite-difference equation. Sib Math J 7, 1074–1083 (1966). https://doi.org/10.1007/BF00966404
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DOI: https://doi.org/10.1007/BF00966404