scholarly journals C0-semigroups of linear operators on some ultrametric Banach spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Toka Diagana
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Crucial Role ◽  
Evolution Equations ◽  
Linear Operators ◽  
Ground Field ◽  
Semigroups Of Linear Operators ◽  
Classical Setting

C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization ofC0-semigroups on (ultrametric) free Banach spacesE. In contrast with the classical setting, the parameter of a givenC0-semigroup belongs to a clopen ballΩrof the ground fieldK. As an illustration, we will discuss the solvability of some homogeneousp-adic differential equations.

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Shengli Xie
Keyword(s):  
Differential Equations ◽  
Differential Evolution ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Existence Results ◽  
Order Case

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.

scholarly journals On the Behaviour of Singular Semigroups in Intermediate and Interpolation Spaces and Its Applications to Maximal Regularity for Degenerate Integro-Differential Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-37 ◽  
Author(s):  
Alberto Favaron ◽  
Angelo Favini
Keyword(s):  
Differential Evolution ◽  
Banach Spaces ◽  
Wide Class ◽  
Evolution Equations ◽  
Maximal Regularity ◽  
Linear Operators ◽  
Interpolation Spaces ◽  
Power Type ◽  
Maximal Time

For those semigroups, which may have power type singularities and whose generators are abstract multivalued linear operators, we characterize the behaviour with respect to a certain set of intermediate and interpolation spaces. The obtained results are then applied to provide maximal time regularity for the solutions to a wide class of degenerate integro- and non-integro-differential evolution equations in Banach spaces.

Sign in / Sign up

Export Citation Format

Share Document