Volterra nonautonomous evolution inclusions: topological structure of solution sets and applications

Abstract

This paper concerns with a class of Volterra nonautonomous evolution inclusions with time delay effect defined on a noncompact interval. It involves a family of (possibly unbounded) operators, which generates a noncompact evolution family. In the framework of Fréchet spaces, the topological structure of the solution set for evolution inclusion is considered. Moreover, we obtain geometric features of the corresponding solution map. Our results extend essentially the existing ones which do not involve Volterra integral in nonlinearity. We finally present a concrete example to illustrate the abstract results.

Keywords:

• Volterra nonautonomous evolution
• fréchet space
• noncompact evolution family
• topological structure
• $R_{\delta }$-map

2010 Mathematics Subject Classifications:

• 35A30
• 35R70
• 45D05

Acknowledgments

The authors are greatly indebted to all those who made suggestions for improvements to this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research leading to the results of this paper has received funding from the NSFC [grant number 12071408], NSF of Jiangsu Province [grant number BK20201149] and the scientific research start funds for Xuzhou University of Technology advanced talents introduction [grant number 02900264].