On the response of autonomous sweeping processes to periodic perturbations
The authors consider an autonomous sweeping process of the form \[ - \dot{u}(t) \in N_B(u(t)) + f_0(u(t)),\,\,u \in \mathbb{R}^2,\tag{1} \] where \(B = \{x \in \mathbb{R}^2: \|x\| \leq 1 \}\) and \(N_B(x) = \{\xi \in \mathbb{R}^2: \langle \xi, c -x \rangle \leq 0 \,\,\forall c \in C \}\) is the outward normal cone to \(B.\) It is supposed that system (1) possesses a boundary equilibrium \(u_\star \in \partial B,\) i.e., \(f_0(u_\star) \in - N_B(u_\star)\) and \(f_0(u_\star) \neq 0\). Sufficient conditions under which the equilibrium \(u_\star\) persists under periodic perturbations \(f_\varepsilon (t,u)\) of \(f_0\) are studied.
scientific article; zbMATH DE number 6678149
scientific article