Existence results for a class of semilinear differential variational inequalities with nonlocal boundary conditions

Zhenhai Liu, Liang Lu, Xiufeng Guo

DOI: http://dx.doi.org/10.12775/TMNA.2019.088


In the paper we study a class of semilinear differential variational systems with nonlocal boundary conditions, which are obtained by mixing evolution equations and generalized variational inequalities. Firstly, we show the properties of the solution set for generalized variational inequalities. Then, the existence results are established and proved mainly by the topological degree theory and the Yosida approximations of the generator of $C_0$-semigroup.


Semilinear differential variational inequalities; existence of mild solutions; topological degree theory; Yosida approximations; nonlocal boundary conditions

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