LYAPUNOV STABILITY FOR MEASURE DIFFERENTIAL EQUATIONS

Recently, the concept of measure differential equation was introduced in B. Piccoli, Measure differential equations, Arch Ration Mech Anal, 233 (2019), 1289-1317. Such a concept allows for deterministic modeling of uncertainty, finite-speed diffusion, concentration, and other phenomena. Moreover, it represents a natural generalization of ordinary differential equations to measures. In this paper, we deal with the stability of fixed points for measure differential equations. In particular, we discuss two concepts related to classical Lyapunov stability in terms of measure support and first moment. The two concepts are not comparable, but the latter implies the former if the measure differential equation is defined by an ordinary one. Finally, we provide results concerning Lyapunov functions