A generalized Gronwall–Bellman–Ou–Iang type inequality for discontinuous functions and applications to BVP

In this paper we investigate a generalized Gronwall–Bellman–Ou–Iang type inequality for piecewise continuous functions. By studying the unknown function in different continuous regions Ωkj of Ω, we give the complete estimate for the unknown function. We apply our result to a boundary value problem of a partial impulsive differential equation for estimation of its solution.