MSC: 34K06
DOI: 10.21538/0134-4889-2025-31-4-106-114
The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations. We show that the obtained oscillation criterion is a generalization of J. S. W. Wong’s oscillation criterion for second order linear nonhomogeneous ordinary differential equations. Two examples, demonstrating the aptitude of the obtained criteria, are presented.
Keywords: Riccati equations, functional-differential equations, oscillation, interval oscillation, non-oscillation
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Received June 27, 2025
Revised August 12, 2025
Accepted August 18, 2025
Gevorg Avagovich Grigorian, Cand. Sci. (Phys.-Math.), PhD, Institute of Mathematics of NAS of Armenia, Yerevan, e-mail: mathphys2@instmath.sci.am
Cite this article as: G.A. Grigorian. Oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 4, pp. 106–114.
Русский
Г.А. Григорян. Критерии колебательности и неколебательности для линейных неоднородных функционально-дифференциальных уравнений второго порядка
Метод уравнения Риккати применяется для установления критериев осцилляционности и неосцилляционности для линейных неоднородных функционально-дифференциальных уравнений второго порядка. Показано, что полученный критерий осцилляционности является обобщением критерия осцилляционности Дж. С. В. Вонга для линейных неоднородных обыкновенных дифференциальных уравнений второго порядка. Приведены два примера, демонстрирующие применимость полученных критериев.
Ключевые слова: уравнения Риккати, функционально-дифференциальные уравнения, колебание, интервальное колебание, отсутствие колебания.
