Stepanov-like pseudo-almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay

2009 ◽  
Vol 71 (11) ◽  
pp. 5381-5391 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Pseudo Almost Periodic

scholarly journals Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Abdelkarim-Nidal Akdad ◽  
Khalil Ezzinbi ◽  
Lotti Souden
Keyword(s):  
Existence Result ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic ◽  
Automorphic Functions

AbstractIn this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

Pseudo Almost Periodicity and Its Applications to Impulsive Nonautonomous Partial Functional Stochastic Evolution Equations

2018 ◽  
Vol 19 (5) ◽  
pp. 511-529
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodicity ◽  
Pseudo Almost Periodic ◽  
Lipschitz Conditions ◽  
Composition Theorem

AbstractIn this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of$p$-mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of$p$-mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results.

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.

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