We study persistence of periodic solutions perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular solution. The results this paper are motivated by result Holmes and Wiggins where authors considered two dimensional Hamiltonian family smooth systems depending on scalar variable which is solution singularly equation.

Sound propagation in uniformly lined straight ducts with uniform mean flow is well established by its analytically exact description in duct modes [1, 2, 3]. In cross-wise nonuniform flow there are still modes, although the (Pridmore-Brown) equation that describes them is in general not solvable in terms of standard functions [4, 5, 6, 7, 8, 9] and has to be solved numerically. These modal solu...

We provide linear approximations to the marginal distributions for a class of infinite-state continuous-time stationary Markov chains in slowly varying environents. We take an approach motivated by light-traffic approximations to stationary point processes, which permits us to consider general stationary environments. Under mild assumptions we show that Jackson networks with routing not affecte...