Estimation of Unknown Function of a Class of Double Integral Inequalities

A class of nonlinear double integral inequalities is studied, which includes an unknown function and its derivative function in integrand function, and a nonconstant factor outside integral sign. The upper bound of the unknown function in the integro-differential inequality is estimated explicitly using the techniques of change of variable, the method of amplification, and inverse function technique. The derived results can be applied in the study of the explicit upper bounds of solutions of a class of integro-differential equations.