Open AccessExistence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron Δ-integrals
Author(s) -
F. Andrade da Silva,
M. Federson,
Eduard Toon
Publication year - 2021
Publication title -
bulletin of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 1664-3607
pISSN - 1664-3615
DOI - 10.1142/s1664360721500119
Subject(s) - mathematics , uniqueness , controllability , classification of discontinuities , constant (computer programming) , mathematical analysis , integral equation , banach space , dynamic equation , nonlinear system , computer science , physics , programming language , quantum mechanics
In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results.