Open AccessNonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions
Author(s) -
Yangyang Yu,
Rong-Nian Wang,
Ioan I. Vrabie
Publication year - 2021
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.2020.065
Subject(s) - mathematics , nonlinear system , dissipative system , operator (biology) , bounded function , contractible space , fixed point theorem , interval (graph theory) , mathematical analysis , pure mathematics , combinatorics , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
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.