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The aim of this work is to give sufficient conditions ensuring that the space PAP(𝕉, X, µ) of µ-pseudo almost periodic functions and the space PAA(𝕉, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(𝕉). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.

In thiswork,we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory.

In thiswork, we provide sufficient conditions ensuring the existence and uniqueness of an Eberlein weakly almost periodic solutions for some semilinear integro-differential equations with infinite delay in Banach spaces. For illustration, we provide an example arising in viscoelasticity theory. [ABSTRACT FROM AUTHOR]

In this article, we prove a number of properties concerning a (new) class of (Stepanov-like) Eberlein-weakly almost periodic (SP-E.w. a. p.) functions with values in a Banach space. We use the results obtained to study the asymptotic behaviour of solutions to the evolution equation:whereAis the generator of an integral resolvent family in a Banach space 𝕏,a ∈ L1(ℝ), andfis a given 𝕏-valued function on ℝ. The objective is to deduce Eberlein-weakly almost periodicity (in Stepanov-like sense) of the solutionufrom corresponding properties on the partf. [ABSTRACT FROM AUTHOR]

By means of the fixed point methods and the properties of the pseudo almost automorphic functions, the existence and uniqueness of pseudo almost automorphic solutions are obtained for differential equations involving reflection of the argument. For the nonscalar, case we use the exponential dichotomy properties. [ABSTRACT FROM AUTHOR]

In this work, we give sufficient conditions for the existence and uniqueness of a weighted pseudo-almost periodic solutions for some neutral partial functional differential equations. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main result, we propose to study the existence and uniqueness of a weighted pseudo-almost periodic solution for some neutral model arising in physical systems. [ABSTRACT FROM AUTHOR]

In this work, we investigate the existence and uniqueness of an almost automorphic solution for some dissipative ordinary and functional differential equations in Banach spaces. We prove the existence and uniqueness of an almost automorphic solution for dissipative differential equations and then we apply this result to show the existence of almost automorphic solutions for some functional differential equations. [ABSTRACT FROM AUTHOR]

We study the convolution of Stepanov-like almost automorphic functions and L¹ functions. Also we consider nonautonomous evolution equations, with a periodic operator coefficient and Stepanov-like almost automorphic forcing, and show that, under certain assumptions, any bounded mild solution is almost automorphic. [ABSTRACT FROM AUTHOR]