scholarly journals Pazy-type characterization for differentiability of propagators of higher order Cauchy problems in Banach spaces

1999 ◽  
Vol 5 (3) ◽  
pp. 651-662
Author(s):  
Ti-Jun Xiao ◽  
◽  
Jin Liang
Keyword(s):  
Banach Spaces ◽  
Higher Order ◽  
Cauchy Problems

scholarly journals Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Rodrigo Ponce
Keyword(s):  
Banach Spaces ◽  
Fractional Derivatives ◽  
Mild Solutions ◽  
Cauchy Problems ◽  
Families Of Operators ◽  
Resolvent Families

We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases0<α<1and1<α<2.

scholarly journals Arbitrarily distortable Banach spaces of higher order

2016 ◽  
Vol 214 (2) ◽  
pp. 553-581 ◽  
Author(s):  
Kevin Beanland ◽  
Ryan Causey ◽  
Pavlos Motakis
Keyword(s):  
Banach Spaces ◽  
Higher Order

scholarly journals Higher order Gateaux smooth bump functions on Banach spaces

1995 ◽  
Vol 51 (2) ◽  
pp. 291-300 ◽  
Author(s):  
David P. McLaughlin ◽  
Jon D. Vanderwerff
Keyword(s):  
Banach Spaces ◽  
Higher Order ◽  
Smooth Approximation ◽  
Bump Function

For Г uncountable and p ≥ 1 odd, it is shown ℓp(г) admits no continuous p-times Gateaux differentiable bump function. A space is shown to admit a norm with Hölder derivative on its sphere if it admits a bounded bump function with uniformly directionally Hölder derivative. Some results on smooth approximation are obtained for spaces that admit bounded uniformly Gateaux differentiable bump functions.

Incomplete Sobolev type equations of higher order with "white noise" in quasi-Banach spaces

2016 ◽  
Vol 10 ◽  
pp. 1811-1819
Author(s):  
Alyona A. Zamyshlyaeva ◽  
Evgeniy V. Bychkov ◽  
Olga N. Tsyplenkova
Keyword(s):  
White Noise ◽  
Banach Spaces ◽  
Higher Order ◽  
Sobolev Type

scholarly journals Spectral Properties and Finite Pole Assignment of Linear Neutral Systems in Banach Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-27 ◽  
Author(s):  
Xuewen Xia ◽  
Kai Liu
Keyword(s):  
Banach Spaces ◽  
Spectral Properties ◽  
Functional Differential Equations ◽  
Pole Assignment ◽  
Neutral System ◽  
Cauchy Problems ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Functional Differential ◽  
Rank Conditions

We will consider a pole assignment problem for a class of linear neutral functional differential equations in Banach spaces. We will think of the neutral system studied as that of involving no time delays and reduce the study of adjoint semigroups and spectral properties of neutral equations to those of Cauchy problems. Under the assumption that both the control and eigenspace of pole are finite dimensional, we establish the rank conditions for finite pole assignability.

scholarly journals On the local convergence of higher order methods in Banach spaces

2021 ◽  
Vol 22 (2) ◽  
pp. 855-870
Author(s):  
Debasis Sharma ◽  
◽  
Sanjaya Kumar Parhi ◽  
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Higher Order ◽  
Higher Order Methods
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