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 Mat. Zametki, 2011, Volume 90, Issue 3, Pages 323–339 (Mi mz3859)

On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order

A. R. Alievab

a Baku State University
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: We obtain sufficient conditions for the regular solvability of initial boundary-value problems for a class of operator-differential equations of third order with variable coefficients on the semiaxis. These conditions are expressed only in terms of the operator coefficients of the equations under study. We obtain estimates of the norms of intermediate derivative operators via the discontinuous principal parts of the equations and also find relations between these estimates and the conditions for regular solvability.

Keywords: operator-differential equation, self-adjoint operator, initial boundary-value problem, Hilbert space, Banach space, Fourier transform, polynomial operator pencil

DOI: https://doi.org/10.4213/mzm3859

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English version:
Mathematical Notes, 2011, 90:3, 307–321

Bibliographic databases:

UDC: 517.946
Revised: 13.01.2011

Citation: A. R. Aliev, “On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order”, Mat. Zametki, 90:3 (2011), 323–339; Math. Notes, 90:3 (2011), 307–321

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz3859
• https://doi.org/10.4213/mzm3859
• http://mi.mathnet.ru/eng/mz/v90/i3/p323

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. S. Mirzoyev, A. R. Aliev, L. A. Rustamova, “Solvability Conditions for Boundary-Value Problems for Elliptic Operator-Differential Equations with Discontinuous Coefficient”, Math. Notes, 92:5 (2012), 722–726
2. P. V. Vinogradova, A. M. Samusenko, “Proektsionnyi metod dlya differentsialno-operatornogo uravneniya tretego poryadka s nelineinym monotonnym operatorom”, Sib. zhurn. industr. matem., 15:4 (2012), 64–70
3. S. S. Mirzoev, A. R. Aliev, L. A. Rustamova, “On the Boundary Value Problem with the Operator in Boundary Conditions for the Operator-Differential Equation of Second Order with Discontinous Coefficients”, Zhurn. matem. fiz., anal., geom., 9:2 (2013), 207–226
4. Aliev A.R., Muradova N.L., “Third-order operator-differential equations with discontinuous coefficients and operators in the boundary conditions”, Electron. J. Differ. Equ., 2013, 219, 13 pp.
5. P. V. Vinogradova, A. G. Zarubin, “Galerkin method for a third-order differential-operator equation”, Differ. Equ., 50:2 (2014), 246–253
6. P. V. Vinogradova, T. E. Koroleva, “One projection method for linear equation of third order”, Russian Math. (Iz. VUZ), 58:11 (2014), 22–27
7. Aliev A.R., Elbably A.L., “on a Class of Operator-Differential Equations of the Third Order With Multiple Characteristics on the Whole Axis in the Weighted Space”, Math. Slovaca, 65:3 (2015), 667–682
8. Aliev A.R., Mirzoev S.S., Soylemezo M.A., “On Solvability of Third-Order Operator Differential Equation With Parabolic Principal Part in Weighted Space”, J. Funct. space, 2017, 2932134
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