Periodic solutions for impulsive differential inclusions with state dependent impulses - Gabor, Grzegorz; Ruszkowski, Sebastian (Topological Methods in Nonlinear Analysis, 2025)
The paper investigates some qualitative properties of solutions to differential inclusions with state-dependent impulses. The first main objective is to prove that the mapping which assigns a set of solutions to the Cauchy problem for a given initial point is upper semicontinuous. This allows us to apply topological degree theory to the multivalued Poincaré operator along trajectories, which is the second main aim of the work, enabling us to establish the existence of periodic solutions. To verify the non-zero value of the topological degree, we utilize a generalized Krasnosel’skiǐ guiding function technique.