Some new nonlinear Gronwall-Bellman-Type integral inequalities and applications to BVPs

In this paper we establish some new nonlinear Gronwall-Bellman-Type integral inequalities with two variables, which include a non-constant term outside the integrals. These inequalities generalize the results in Chen et al. (J. Inequal. Appl. 2009:258569, 15 p., 2009). We apply our result to a boundary value problem of a partial differential equation for boundedness, uniqueness and continuous dependence.