Stepanov-like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations

2012 ◽  
Vol 75 (1) ◽  
pp. 244-252 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equations ◽  
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.

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