Weak solutions of a hyperbolic-type partial dynamic equation in Banach spaces

Abstract

In this article we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation (Fourmula presented) in Banach spaces. For this purpose by generalizing the definitions and results of Cichoń et.al. we develop weak partial derivatives double integrability and the mean value results for double integrals on time scales. DeBlasi measure of weak noncompactness and Kubiaczyk’s fixed point theorem for the weakly sequentially continuous mappings are the essential tools to prove the main result. © 2020 Elsevier B.V. All rights reserved.