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2021 Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions
Yang-Yang Yu, Rong-Nian Wang, Ioan I. Vrabie
Topol. Methods Nonlinear Anal. 58(1): 135-160 (2021). DOI: 10.12775/TMNA.2020.065

Abstract

This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.

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Yang-Yang Yu. Rong-Nian Wang. Ioan I. Vrabie. "Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions." Topol. Methods Nonlinear Anal. 58 (1) 135 - 160, 2021. https://doi.org/10.12775/TMNA.2020.065

Information

Published: 2021
First available in Project Euclid: 21 September 2021

Digital Object Identifier: 10.12775/TMNA.2020.065

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.58 • No. 1 • 2021
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