Maximal regularity in lp spaces for discrete time fractional shifted equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Lizama, Carlos¹  Murillo-Arcila, Marina² 

[1] Univ Santiago Chile, Fac Ciencias, Dept Matemet & Ciencia Computac, Casilla 307,Correo 2, Santiago, Chile

[2] Basque Ctr Appl Math, Mazarredo 14, E-48009 Bilbao, Basque Country, Spain

关键词: Maximal l(p)-regularity;    Shifted equations;    Discrete time;    Grunwald-Letnikov derivative;   

DOI  :  10.1016/j.jde.2017.04.035

来源: Elsevier

【 摘 要 】

In this paper, we are presenting a new method based on operator-valued Fourier multipliers to characterize the existence and uniqueness of l(p)-solutions for discrete time fractional models in the form Delta(alpha)u(n,x) = Au(n,x) + Sigma(k)(j=1) beta(j)u(n - iota(j),x) + f (n,u(n, x)), n is an element of Z, x is an element of Omega subset of R-N , beta(j) is an element of R and iota(j) is an element of Z, where A is a closed linear operator defined on a Banach space X and Delta(alpha) denotes the Grunwald-Letnikov fractional derivative of order alpha > 0. If X is a UMD space, we provide this characterization only in terms of the R-boundedness of the operator-valued symbol associated to the abstract model. To illustrate our results, we derive new qualitative properties of nonlinear difference equations with shiftings, including fractional versions of the logistic and Nagumo equations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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