Conditions of coercive solvability of third-order differential equation with unbounded intermediate coefficients

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dc.contributor.author Ospanov, K.N.
dc.contributor.author Yeskabylova, Zh.B.
dc.date.accessioned 2019-08-19T10:57:50Z
dc.date.available 2019-08-19T10:57:50Z
dc.date.issued 2019-06-28
dc.identifier.citation Ospanov, K.N. Conditions of coercive solvability of third-order differential equation with unbounded intermediate coefficients / K.N. Ospanov, Zh.B. Yeskabylova // Қарағанды универисетінің хабаршысы. Математика сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series. – 2019. - № 2. – P. 56-69. ru_RU
dc.identifier.issn 2518-7929
dc.identifier.issn 2663-5011
dc.identifier.uri http://rep.ksu.kz//handle/data/7270
dc.description.abstract In this paper we study the following equation -y’’’ + r (x) y’’ + q (x) y’ + s (x) y = f (x); where the intermediate coefficients r and q do not depend on s. We give the conditions of the coercive solvability for f E L2 (–8; +8) of this equation. For the solution y, we obtained the following maximal regularity estimate: IIy’’’II2 + IIry’’II2 + IIqy’II2 + IIsyII2 ≤ C IIfII2; where II . II2 is the norm of L2 (-8; +8). This estimate is important for study of the qwasilinear third-order differential equation in (-8; +8). We investigate some binomial degenerate differential equations and we prove that they are coercive solvable. Here we apply the method of the separability theory for differential operators in a Hilbert space, wich was developed by M. Otelbaev. Using these auxillary statements and some well-known Hardy type weighted integral inequalities, we obtain the desired result. In contrast to the preliminary results, we do not assume that the coefficient s is strict positive, the results are also valid in the case that s = 0. ru_RU
dc.language.iso en ru_RU
dc.publisher Ye.A.Buketov Karaganda State University Publishing house ru_RU
dc.relation.ispartofseries Қарағанды универисетінің хабаршысы. Математика Сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series.;№ 2(94)/2019
dc.subject differential equation ru_RU
dc.subject unbounded coefficients ru_RU
dc.subject maximal regularity ru_RU
dc.subject separability ru_RU
dc.title Conditions of coercive solvability of third-order differential equation with unbounded intermediate coefficients ru_RU
dc.title.alternative Аралық коэффициенттері шенелмеген үшінші ретті дифференциалдық теңдеудің коэрцитивті шешілу шарттары ru_RU
dc.title.alternative Условия коэрцитивной разрешимости дифференциального уравнения третьего порядка с неограниченными промежуточными коэффициентами ru_RU
dc.type Article ru_RU


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