Abstract
Abstract 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 ∈ L 1(). 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.
Highlights
The aim of this work is to give su cient conditions ensuring that the space PAP(R, X, μ) of μ-pseudo almost periodic functions and the space PAA(R, X, μ) of μ-pseudo almost automorphic functions are invariant by the convolution product ζf = k * f, k ∈ L (R)
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 di erential equations
Introduction μ-pseudo almost periodic functions and μ-pseudo almost automorphic functions have been studied by several authors in the last decade
Summary
Since k * g is almost periodic (respectively almost automorphic) [1, 2], the following two assertions are equivalent: (i) PAP(R, X, μ) or PAA(R, X, μ) is convolution invariant. We investigate the existence and uniqueness of μ-pseudo almost periodic (respectively μpseudo almost automorphic) mild solutions to the following equations: t u(t) = R(t, s)f (s, u(s))ds,
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