Existence results of semilinear differential variational inequalities without compactness

ABSTRACT

The purpose of this paper is to study a class of semilinear differential variational systems with nonlocal boundary conditions, which are obtained by mixing semilinear evolution equations and generalized variational inequalities. First we prove essential properties of the solution set for generalized variational inequalities. Then without requiring any compactness condition for the evolution operator or for the nonlinear term, two existence results for mild solutions are established by applying a weak topology technique combined with a fixed point theorem.

KEYWORDS:

• Semilinear evolution equation and inclusion
• generalized variational inequality
• existence of mild solution
• weak topology technique
• nonlocal boundary condition

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34L30
• 47D03

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This project supported by National Natural Science Foundation of China Grant No. 11671101, Guangxi Natural Science Foundation under Grant Nos. 2018GXNSFDA138002, 2017GXNSFBA198031, Project of Guangxi Education Department [grant number2017KY0648], Hundred Talent Program for Introducing the Overseas High-Level Talents of Guangxi colleges and Universities. The project has also received funding from the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH. The third author is also partially supported by CNPq/BRAZIL PROC. 400633/2017-5.