Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory

Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

In recent years, the theory of almost automorphic functions has been developed extensively see, e.g., Bugajewski and N’guérékata 1 , Cuevas and Lizama 2 , and N’guérékata 3 and the references therein . However, literature concerning pseudo-almost automorphic functions is very new cf. 4 . It is well known that the study of composition of two functions with special properties is important and bas...

Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales

* Correspondence: [email protected]. cn Department of Mathematics, Yunnan University Kunming, Yunnan 650091, People’s Republic of China Abstract In this paper, we first introduce a concept of the mean-value of uniformly almost periodic functions on time scales and give some of its basic properties. Then, we propose a concept of pseudo almost periodic functions on time scales and study some basic pr...

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

where A t for t ∈ R is a family of closed linear operators with domains D A t satisfying Acquistapace-Terreni conditions, and the function f : R × X → X is almost automorphic in t ∈ R uniformly in the second variable, was studied. For that, the author made extensive use of techniques utilized in 2 , exponential dichotomy tools, and the Schauder fixed point theorem. In this paper we study the ex...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

Evolution Equations in Generalized Stepanov-like Pseudo Almost Automorphic Spaces

In this article, first we introduce and study the concept of Sγ pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in Sγ -pseudo almost automorphic spaces. T...