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