In this paper, we aim to study a stochastic process from macro point of view, and thus, periodic solution in distributional sense is introduced. We first give the definition then establish existence on bounded domain. Lastly, for case that probability density function exists, obtain solutions corresponding by using technique deterministic partial differential equations.

We study the time-periodic solutions to systems of conservation laws with ellipticity. It is shown that under time-periodic boundary condition, the system admits at least one global time-periodic solution bounded uniformly with the same period.

Let T be a periodic time scale. We use Krasnoselskii’s fixed point theorem to show that the neutral functional differential equation with impulses x(t) = −A(t)x(t) + g(t, x(t− h(t))) + f(t, x(t), x(t− h(t))), t 6= tj , t ∈ T, x(t+j ) = x(t − j ) + Ij(x(tj)), j ∈ Z + has a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contrac...