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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

  • ---
  • [1] Amann H., Maximal regularity for non-autonomous evolution equations. Advanced Nonlinear Studies, (2004) 4, 417-430.
  • [2] Agranovich M. S., Spectral boundary value problems in Lipschitz domains for strongly elliptic systems in Banach spaces Hpơ p and Bơ; Funct. Anal. Appl., (2008) 42(4), 249–267. [Crossref]
  • [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 operator equations, 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.), Lecture Notes 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-operator equations 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.
  • [12] Goldstain J. A., Semigroups of Linear Operators and Applications, Oxford University Press, Oxfard, 1985.
  • [13] Krein S. G., Linear Differential Equations in Banach space, American Mathematical Society, Providence, 1971.
  • [14] Lunardi A., Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhauser, 2003.
  • [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, Nonlinear Anal. 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 an annuals, 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, Nonlinear Anal. Real World Appl., (2010), 11(2), 932-951. [WoS]
  • [24] Triebel H., Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
  • [25] Triebel H., Spaces of distributions with weights. Multiplier on Lp spaces with weights. Math. Nachr., (1977)78, 339-356. [Crossref]
  • [26] Weis L, Operator-valued Fourier multiplier theorems and maximal Lp regularity, Math. Ann., (2001), 319, 735-758.
  • [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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