Estimates for Solutions of Differential Equations in a Banach Space via Commutators

Estimates for Solutions of Differential Equations in a Banach Space via Commutators References[1] V.M. Aleksandrov and E.V. Kovalenko, Problems in Continuous Mechanics with Mixed Boundary Conditions, Nauka, Moscow 1986. In Russian.[2] J.A.D. Appleby and D.W. Reynolds, On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro-differential equations, Journal of Integral Equations and Applications, 14, no 2 (2002), 521-543.[3] M.C. Cercignani, Mathematical Methods in Kinetic Theory, Macmillian, New York, 1969.[4] Chuhu Jin and Jiaowan Luo, Stability of an integro-differential equation, Computers and Mathematics with Applications, 57 (2009) 1080-1088.[5] Yu L. Daleckii, and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer.Math. Soc., Providence, R. I. 1974.[6] J.D. Dollard and Ch. N. Friedman, Product Integration with Applications to Differential Equations. Encyclopedia ofMathematics and its applications; v.10., London, Addison-Wesley Publ. Company, 1979. [7] A. Domoshnitsky and Ya. Goltser, An approach to study bifurcations and stability of integro-differential equations. Math. Comput. Modelling, 36 (2002), 663-678.[8] A.D. Drozdov, Explicit stability conditions for integro-differential equations with periodic coeflcients, Math. Methods Appl. Sci. 21 (1998), 565-588.[9] A.D. Drozdov and M. I. Gil’, Stability of linear integro-differential equations with periodic coeflcients. Quart. Appl. Math. 54 (1996), 609-624.10.1090/qam/1417227[10] N.T. Dung, On exponential stability of linear Levin-Nohel integro-differential equations, Journal of Mathematical Physics 56, 022702 (2015); doi: 10.1063/1.4906811[11] F.R. Gantmakher, Theory of Matrices. Nauka, Moscow, 1967. In Russian.[12] M.I. Gil’, Operator Functions and Localization of Spectra, Lecture Notes In Mathematics vol. 1830, Springer-Verlag, Berlin, 2003.[13] M.I. Gil’, Spectrum and resolvent of a partial integral operator. Applicable Analysis, 87, no. 5, (2008) 555-566.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000256805300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3[14] M.I. Gil’, On stability of linear Barbashin type integro-differential equations, Mathematical Problems in Engineering, 2015, Article ID 962565, (2015), 5 pages.[15] M.I. Gil’, A bound for the Hilbert-Schmidt norm of generalized commutators of nonself-adjoint operators, Operators and Matrices, 11, no. 1 (2017), 115-123[16] Ya. Goltser and A. Domoshnitsky, Bifurcation and stability of integrodifferential equations, Nonlinear Anal. 47 (2001), 953-967.[17] H.G. Kaper, C.G. Lekkerkerker, and J. Hejtmanek, Spectral Methods in Linear Transport Theory, Birkhauser, Basel, 1982.[18] W.J. Rugh, Linear System Theory. Prentice Hall, Upper Saddle River, New Jersey, 1996.[19] H. R. Thieme, A differential-integral equation modelling the dynamics of populations with a rank structure, Lect. Notes Biomath. 68 (1986), 496-511[20] J. Vanualailai and S. Nakagiri, Stability of a system of Volterra integro-differential equations J. Math. Anal. Appl. 281 (2003) 602-619[21] B. Zhang, Construction of Liapunov functionals for linear Volterra integrodifferential equations and stability of delay systems, Electron. J. Qual. Theory Differ. Equ. 30 (2000) 1-17. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonautonomous and Stochastic Dynamical Systems de Gruyter

Estimates for Solutions of Differential Equations in a Banach Space via Commutators

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De Gruyter Open
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© 2018
ISSN
2299-3258
eISSN
2353-0626
D.O.I.
10.1515/msds-2018-0001
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Abstract

References[1] V.M. Aleksandrov and E.V. Kovalenko, Problems in Continuous Mechanics with Mixed Boundary Conditions, Nauka, Moscow 1986. In Russian.[2] J.A.D. Appleby and D.W. Reynolds, On the non-exponential convergence of asymptotically stable solutions of linear scalar Volterra integro-differential equations, Journal of Integral Equations and Applications, 14, no 2 (2002), 521-543.[3] M.C. Cercignani, Mathematical Methods in Kinetic Theory, Macmillian, New York, 1969.[4] Chuhu Jin and Jiaowan Luo, Stability of an integro-differential equation, Computers and Mathematics with Applications, 57 (2009) 1080-1088.[5] Yu L. Daleckii, and M. G. Krein, Stability of Solutions of Differential Equations in Banach Space, Amer.Math. Soc., Providence, R. I. 1974.[6] J.D. Dollard and Ch. N. Friedman, Product Integration with Applications to Differential Equations. Encyclopedia ofMathematics and its applications; v.10., London, Addison-Wesley Publ. Company, 1979. [7] A. Domoshnitsky and Ya. Goltser, An approach to study bifurcations and stability of integro-differential equations. Math. Comput. Modelling, 36 (2002), 663-678.[8] A.D. Drozdov, Explicit stability conditions for integro-differential equations with periodic coeflcients, Math. Methods Appl. Sci. 21 (1998), 565-588.[9] A.D. Drozdov and M. I. Gil’, Stability of linear integro-differential equations with periodic coeflcients. Quart. Appl. Math. 54 (1996), 609-624.10.1090/qam/1417227[10] N.T. Dung, On exponential stability of linear Levin-Nohel integro-differential equations, Journal of Mathematical Physics 56, 022702 (2015); doi: 10.1063/1.4906811[11] F.R. Gantmakher, Theory of Matrices. Nauka, Moscow, 1967. In Russian.[12] M.I. Gil’, Operator Functions and Localization of Spectra, Lecture Notes In Mathematics vol. 1830, Springer-Verlag, Berlin, 2003.[13] M.I. Gil’, Spectrum and resolvent of a partial integral operator. Applicable Analysis, 87, no. 5, (2008) 555-566.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000256805300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3[14] M.I. Gil’, On stability of linear Barbashin type integro-differential equations, Mathematical Problems in Engineering, 2015, Article ID 962565, (2015), 5 pages.[15] M.I. Gil’, A bound for the Hilbert-Schmidt norm of generalized commutators of nonself-adjoint operators, Operators and Matrices, 11, no. 1 (2017), 115-123[16] Ya. Goltser and A. Domoshnitsky, Bifurcation and stability of integrodifferential equations, Nonlinear Anal. 47 (2001), 953-967.[17] H.G. Kaper, C.G. Lekkerkerker, and J. Hejtmanek, Spectral Methods in Linear Transport Theory, Birkhauser, Basel, 1982.[18] W.J. Rugh, Linear System Theory. Prentice Hall, Upper Saddle River, New Jersey, 1996.[19] H. R. Thieme, A differential-integral equation modelling the dynamics of populations with a rank structure, Lect. Notes Biomath. 68 (1986), 496-511[20] J. Vanualailai and S. Nakagiri, Stability of a system of Volterra integro-differential equations J. Math. Anal. Appl. 281 (2003) 602-619[21] B. Zhang, Construction of Liapunov functionals for linear Volterra integrodifferential equations and stability of delay systems, Electron. J. Qual. Theory Differ. Equ. 30 (2000) 1-17.

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Nonautonomous and Stochastic Dynamical Systemsde Gruyter

Published: Feb 28, 2018

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