A generalized nonlinear gronwall-bellman inequality with maxima in two variables

This paper deals with a generalized form of nonlinear retarded gronwall-bellman type integral inequality in which the maximum of the unknown function of two variables is involved. this form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. requiring neither monotonicity nor separability of given functions,we apply a technique of monotonization to estimate the unknown function. our result can be used to weaken conditions for some known results. we apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness. © 2013 yong yan.