scholarly journals Discrete Weighted Pseudo-Almost Automorphy and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhinan Xia
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Convolution Type ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Volterra Difference Equations

We deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.

scholarly journals Weighted Pseudo Almost Automorphic Solutions to Nonautonomous Semilinear Differential Equations

2017 ◽  
Vol 1 (1) ◽  
pp. 27-32
Author(s):  
Saud M. Alsulami
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Evolution Family ◽  
Almost Automorphic ◽  
Exponentially Stable ◽  
Semilinear Differential Equation ◽  
Pseudo Almost Automorphic

We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutionsto the non-autonomous semilinear differential equation in a Banach space X :( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t Rwhere A(t), t R, generates an exponentially stable evolution family {U(t, s)} andf :R X X satisfies a Lipschitz condition with respect to the second argument.MSC 2010: 43A60; 34G20, 47Dxx

Stabilities in Volterra difference equations on a Banach space

2004 ◽  
pp. 159-175 ◽  
Author(s):  
Tetsuo Furumochi ◽  
Satoru Murakami ◽  
Yutaka Nagabuchi
Keyword(s):  
Banach Space ◽  
Difference Equations ◽  
Volterra Difference Equations

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 Discrete Weighted Pseudo Almost Automorphic Solutions of Nonautonomous Difference Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Xiaoqing Wen ◽  
Hongwei Yin
Keyword(s):  
Difference Equations ◽  
Automorphic Function ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic

We introduce the concept of a discrete weighted pseudo almost automorphic function and prove some basic results. Further, we investigate the nonautonomous linear and semilinear difference equations and obtain the weighted pseudo almost automorphic solutions of both these kinds of difference equations, respectively. Our results generalize the ones by Lizama and Mesquita (2013).

scholarly journals (Weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by levy noise

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2403-2424
Author(s):  
Min Yang
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Analysis ◽  
Contraction Principle ◽  
Lévy Noise ◽  
Almost Automorphic ◽  
Fractional Stochastic Differential Equations ◽  
Pseudo Almost Automorphic

In this paper, by using contraction principle, fractional calculus and stochastic analysis, we study the existence and uniqueness of (weighted pseudo) almost automorphic solutions in distribution for fractional stochastic differential equations driven by L?vy noise. An example is presented to illustrate the application of the abstract results.

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