A note on discrete maximal regularity for functional difference equations with infinite delay

Cuevas, Claudio; Vidal, Cláudio

doi:10.1155/ade/2006/97614

Cited by 14 publications

(10 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [20], Kovács, Li and Lubich showed that for a parabolic problem with maximal L p -regularity, the time discretization by a linear multistep method has maximal p -regularity if the method is stable. Finally, Cuevas and Vidal [13] incorporated the delay in the research of maximal p -regularity of discrete time equations.…”

Section: Introductionmentioning

confidence: 99%

Maximal regularity in l spaces for discrete time fractional shifted equations

Lizama

Murillo‐Arcila

2017

Journal of Differential Equations

View full text Add to dashboard Cite

In this paper, we are presenting a new method based on operator-valued Fourier multipliers to characterize the existence and uniqueness of p -solutions for discrete time fractional models in the formwhere A is a closed linear operator defined on a Banach space X and ∆ α denotes the Grünwald-Letnikov fractional derivative of order α > 0. If X is a U M D 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Maximal regularity in l spaces for discrete time fractional shifted equations

Lizama

Murillo‐Arcila

2017

Journal of Differential Equations

View full text Add to dashboard Cite

show abstract

“…[37], maximal regularity for linear parabolic difference equations is treated; recently, discrete maximal regularity for functional difference equations with infinite delay was considered in Ref. [31].…”

Section: Introductionmentioning

confidence: 99%

“…These processes are encountered for example in mathematical models in population dynamics as well as in models of propagation of perturbation in matter with memory. In this direction Cuevas and Vidal [31], considered maximal regularity for Volterra difference equations with infinite delay.…”

Section: Introductionmentioning

confidence: 99%

Perturbation theory, stability, boundedness and asymptotic behaviour for second order evolution equation in discrete time

Castro

Cuevas

2011

Journal of Difference Equations and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [26], maximal regularity for linear parabolic difference equations is treated while in [21,22] the authors has made a perturbation theory for semilinear evolution equations on discrete time for first and second order using discrete maximal regularity; see also the recent paper by Kalton and Portal [30], where they discussed maximal regularity of power-bounded operators and relate the discrete to the continuous time problem for analytic semigroups. Recently, discrete maximal regularity for functional difference equations with infinite delay was considered in [20]. There, applications to Volterra difference equations with infinite delay are also shown.…”

Section: Introductionmentioning

confidence: 99%