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2015 | 13 | 1 |
Tytuł artykułu

Linear and nonlinear abstract differential equations of high order

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-20
zaakceptowano
2015-07-16
online
2015-08-14
Twórcy
  • Okan University, Department of Mechanical Engineering, Akfirat, Tuzla 34959 Istanbul,
    Turkey
  • Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences,
Bibliografia
  • ---
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  • [3] Arendt W., Duelli, M., Maximal Lp- regularity for parabolic and elliptic equations on the line, J. Evol. Equ. (2006), 6(4), 773-790.[Crossref]
  • [4] Agarwal R., Bohner M., Shakhmurov V. B., Linear and nonlinear nonlocal boundary value problems for differential operatorequations, Appl. Anal., (2006), 85(6-7), 701-716.
  • [5] Ashyralyev A, Cuevas. C and Piskarev S., On well-posedness of difference schemes for abstract elliptic problems in spaces,Numer. Func. Anal. Opt., (2008)29, (1-2), 43-65.[WoS][Crossref]
  • [6] Bourgain, J., Some remarks on Banach spaces in which martingale difference sequences are unconditional, Arkiv Math.(1983)21, 163-168.
  • [7] Burkholder D. L., A geometrical conditions that implies the existence certain singular integral of Banach space-valued functions,Proc. Conf. Harmonic Analysis in Honor of Antonu Zigmund, Chicago, 1981,Wads Worth, Belmont, (1983), 270-286.
  • [8] Dore, G., Lp-regularity for abstract differential equations. In: Functional Analysis and Related Topics, H. Komatsu (ed.), LectureNotes in Math. 1540. Springer, 1993.
  • [9] Denk R., Hieber M., Prüss J., R-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Mem. Amer. Math.Soc. (2003), 166 (788), 1-111.
  • [10] Favini A., Shakhmurov V., Yakubov Y., Regular boundary value problems for complete second order elliptic differential-operatorequations in UMD Banach spaces, Semigroup Form, (2009), 79 (1), 22-54.
  • [11] Favini, A., Yagi, A., Degenerate Differential Equations in Banach Spaces, Taylor & Francis, Dekker, New-York, 1999.
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  • [15] Lions J. L., Peetre J., Sur one classe d’espases d’interpolation, IHES Publ. Math. (1964)19, 5-68.
  • [16] Shklyar, A.Ya., Complete second order linear differential equations in Hilbert spaces, Birkhauser Verlak, Basel, 1997.
  • [17] Sobolevskii P. E., Coerciveness inequalities for abstract parabolic equations, Dokl. Akad. Nauk, (1964), 57(1), 27-40.
  • [18] Shahmurov R., On strong solutions of a Robin problem modeling heat conduction in materials with corroded boundary, NonlinearAnal. Real World Appl., (2011),13(1), 441-451.[WoS]
  • [19] Shahmurov R., Solution of the Dirichlet and Neumann problems for a modified Helmholtz equation in Besov spaces on anannuals, J. Differential Equations, 2010, 249(3), 526-550.
  • [20] Shakhmurov V. B., Estimates of approximation numbers for embedding operators and applications, Acta. Math. Sin., (Engl. Ser.),(2012), 28 (9), 1883-1896.[Crossref]
  • [21] Shakhmurov V. B., Degenerate differential operators with parameters, Abstr. Appl. Anal., (2007), 2006, 1-27.[Crossref]
  • [22] Shakhmurov V. B., Regular degenerate separable differential operators and applications, Potential Anal., (2011), 35(3), 201-212.
  • [23] Shakhmurov V. B., Shahmurova A., Nonlinear abstract boundary value problems atmospheric dispersion of pollutants, NonlinearAnal. Real World Appl., (2010), 11(2), 932-951.[WoS]
  • [24] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
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  • [27] Yakubov S. and Yakubov Ya., Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall/CRC, Boca Raton, 2000.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0044
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