Integral equations in the study of the asymptotic behavior of skew-product flows

Abstract

The aim of this paper is to present an inedit perspective concerning the study of the asymptotic behavior of variational systems, using distinct techniques compared with those in the existing literature. We give new and complete answers concerning the study of exponential dichotomy of skew-product flows in terms of the solvability of integral equations between L^p-spaces, motivating the techniques by illustrative examples. We present a comparative analysis between the integral admissibility on the real line and on the half-line, pointing out the main differences as well as the advantages of each case.