Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations

2009 ◽  
Vol 71 (5-6) ◽  
pp. 2349-2360 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

scholarly journals Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equation ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Existence And Uniqueness Theorem ◽  
Abstract Result ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation(d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ,under some assumptions. To illustrate our abstract result, a concrete example is given.

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.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

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