mathematicsВестник российских университетов. МатематикаRussian Universities Reports. Mathematics2686-96672782-3342Тамбовский государственный университет имени Г.Р. Державина10.20310/2686-9667-2020-25-130-123-130mathematics-214Research ArticleСТАТЬИARTICLESО спектральных свойствах и положительности решений периодической краевой задачи для функционально-дифференциального уравнения второго порядкаOn the spectral properties and positivity of solutions of a periodic boundary value problem for a second-order functional differential equationАлвешМануэль ЖоакимAlvesManuel J.mjalves@gmail.comЛабовскийСергей МихайловичLabovskiySergey M.labovski@gmail.comУниверситет имени Эдуардо МондланеРоссияEduardo Mondlane UniversityRussian FederationФГБОУ ВО «Российский экономический университет им. Г.В. Плеханова»РоссияPlekhanov Russian University of EconomicsRussian Federation20201607202025130123130Copyright © Алвеш М.Ж., Лабовский С.М., 20202020Алвеш М.Ж., Лабовский С.М.Alves M.J., Labovskiy S.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathematics.elpub.ru/jour/article/view/214

Для функционально-дифференциального оператора Lu = (1/ρ) -(pu')' + 0 l u(s) d s r(x, s) с симметрией показаны полнота и ортогональность собственных функций. Получены условия положительности функции Грина периодической краевой задачи

For a functional-differential operator Lu = (1/ρ) -(pu')' + 0 l u(s) d s r(x, s) with symmetry, the completeness and orthogonality of the eigenfunctions is shown. The positivity conditions of the Green function of the periodic boundary value problem are obtained.

положительные решенияспектральные свойстваpositive solutionsspectral propertiesReferencesS. Labovskiy, “On spectral problem and positive solutions of a linear singular functionaldifferential equation”, Functional Differential Equations, 20:3-4 (2013), 179-200.S. Labovskiy, “On spectral problem and positive solutions of a linear singular functionaldifferential equation”, Functional Differential Equations, 20:3-4 (2013), 179-200.S.M. Labovski˘ı, “On the Sturm-Liouville problem for a linear singular functional-differential equation”, Russ. Math., 40:11 (1996), 50-56.S.M. Labovski˘ı, “On the Sturm-Liouville problem for a linear singular functional-differential equation”, Russ. Math., 40:11 (1996), 50-56.S. Labovskii, “Little vibrations of an abstract mechanical system and corresponding eigenvalue problem”, Functional Differential Equations, 6:1-2 (1999), 155-167.S. Labovskii, “Little vibrations of an abstract mechanical system and corresponding eigenvalue problem”, Functional Differential Equations, 6:1-2 (1999), 155-167.N. V. Azbelev, V.P. Maksimov, L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations. Methods and Applications., Hindawi Publishing Corporation, New York, 2007.N. V. Azbelev, V.P. Maksimov, L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations. Methods and Applications., Hindawi Publishing Corporation, New York, 2007.

The authors declare that there are no conflicts of interest present.