Uniqueness and Hyers-Ulam stability results for differential variational inequalities with nonlocal conditions
Let \(H_1,\) \(H_2\) be Hilbert spaces; \(K \subset H_2\) a closed convex subset. The authors study the existence and uniqueness of a solution and the Hyers-Ulam stability of a differential variational inequality of the following form \[ \left\{ \begin{array}{l} x^\prime(t) = f(t,x(t),u(t)), \qquad \quad \;\, t \in I :=[0,T]; \\ \langle v - u(t), g(x(t),u(t))\rangle \geq 0, \quad \forall t \in I, \forall v \in K;\\ u(t) \in K. \qquad \qquad \qquad \qquad \quad \, \forall t \in I, \end{array} \right. \] with the initial condition \[ x(0) = x_0 + h(x), \] where \(f \colon I \times H_1 \times K \to H_1,\) \(g \colon H_1 \times K \to H_2\) and \(h \colon C(I,H_1) \to H_1\) are given maps. As applications, a linear differential complimentarity system and a price control model are presented.
scientific article; zbMATH DE number 7491023
scientific article