Singularly perturbed functional-differential inclusions
The following singularly perturbed system of functional differential inclusions with state constraints is considered: \[ (x'(t), \varepsilon y'(t))\in F(t, x(t), y(t), x_t, y_t),\quad x(t)\in K_1,\;y(t)\in K_2, \] where \(K_1\), \(K_2\) are closed convex sets and \(x\in \mathbb{R}^n\), \(y\in \mathbb{R}^m\). Conditions on \(F\) are given which guarantee that the solution set \(Z(\varepsilon)\) of the above problem is either upper semicontinuous at \(\varepsilon= 0^+\) in \(C(I, \mathbb{R}^n)\times L^2(I, \mathbb{R}^m)\)-weak topology or it is lower semicontinuous with respect to \(C(I, \mathbb{R}^n)\times L^1(\mathbb{R}^m)\) topology.
singularly perturbed system of functional differential inclusions with state constraints
scientific article; zbMATH DE number 815977