Abstract
A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.
Highlights
We introduce the following class of differential variational inequalities (DVIs) governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces: Citation: Treanţă, S
In this paper, based on the Browder’s theorem, optimal control theory, KKM theorem, measurability of set-valued mappings and the theory of semigroups, we study the existence of solutions associated with DVI in separable reflexive Banach spaces of infinite dimension
We study the existence of solutions for DVI in infinite-dimensional
Summary
We introduce the following class of differential variational inequalities (DVIs) governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces: Citation: Treanţă, S. A.e. τ ∈ [0, T ], x (0) = x0 , where S(Ω, g(τ, x (τ )) + F (·), ξ ) denotes the solution set of the following variational inequality (VI): find u : [0, T ] → Ω such that h g(τ, x (τ )) + F (u(τ )), v − u(τ )i + ξ (v) − ξ (u(τ )) ≥ 0, In this paper, based on the Browder’s theorem, optimal control theory, KKM theorem, measurability of set-valued mappings and the theory of semigroups, we study the existence of solutions associated with DVI in separable reflexive Banach spaces of infinite dimension.
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