Journal
JOURNAL OF MATHEMATICAL INEQUALITIES
Volume 15, Issue 3, Pages 1031-1045Publisher
ELEMENT
DOI: 10.7153/jmi-2021-15-70
Keywords
Nonlinear system; evolution equation; variational inequality; mild solution
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Funding
- NNSF of China [11761011]
- NSF of Guangxi [2020GXNSFAA297010]
- Guangxi College Young and Middle-aged Teachers Basic Ability Promotion Project [2021KY0651]
- Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing
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This paper deals with abstract second order nonlinear evolution differential equations subject to generalized mixed variational inequalities. By applying Ky Fan inequality theorem, it is proven that the solution set of variational inequalities is bounded, closed and convex, without the rigid restriction of monotonicity. Additionally, the existence of solutions for a class of nonlinear differential equations is discussed.
In this paper, we deal with the system formulated by abstract second order nonlinear evolution differential equations which are subject to a generalized mixed variational inequalities. Firstly, based on Ky Fan inequality theorem, we examine that the solution set of variational inequalities is bounded, closed and convex by getting rid of the rigid restriction of monotonicity. Afterwards, the existence of solutions for a class of nonlinear differential equation is discussed.
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