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Mat. Zametki:

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

This article is cited in 8 scientific papers (total in 8 papers)

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


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

Bibliographic databases:

UDC: 517.946
Received: 02.05.2007
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
\by A.~R.~Aliev
\paper On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 3
\pages 323--339
\jour Math. Notes
\yr 2011
\vol 90
\issue 3
\pages 307--321

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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  mathnet  mathscinet
    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  mathnet  mathscinet
    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.  mathscinet  zmath  isi
    5. P. V. Vinogradova, A. G. Zarubin, “Galerkin method for a third-order differential-operator equation”, Differ. Equ., 50:2 (2014), 246–253  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    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  mathnet  crossref
    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  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
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