Weyl almost periodic solutions to abstract linear and semilinear equations with Weyl almost periodic coefficients

TL;DR

This paper investigates the existence and uniqueness of bounded Weyl almost periodic solutions for abstract linear and semilinear differential equations with Weyl almost periodic coefficients in Banach spaces, including nonautonomous cases.

Contribution

It establishes conditions for the existence and uniqueness of Weyl almost periodic solutions in abstract differential equations with Weyl almost periodic coefficients, extending previous results.

Findings

Proves existence of solutions under certain stability conditions.

Shows uniqueness of solutions in the Weyl almost periodic framework.

Extends analysis to nonautonomous differential equations.

Abstract

In this work, we study the existence and uniqueness of bounded Weyl almost periodic solution to the abstract differential equation u ' (t) = Au(t) + f (t), t $\in$ R, in a Banach space X, where A : D (A) $\subset$ X $\rightarrow$ X is a linear operator (unbounded) which generates an exponentially stable C 0-semigroup on X and f : R $\rightarrow$ X is a Weyl almost periodic function. We also investigate the nonautonomous case.