Retarded Integral Inequality With Multiple Nonlinear Terms and Its Application

On the basis of[Agarwal et al.,J.Inequ.Appl.,2008,Art.ID 908784,15 pages] and[Chen et al.,J.Inequ.Appl.,2009,Art.ID 258569,15 pages],this paper establishes a new nonlinear retarded integral inequality.In the first literature the unknown function u of the inequality is a single variable function,the first term of the right hand of the inequality is positive constant c;in the second literature the first term of the right hand of the inequality is also a positive constant,and the integrand of the second term only contains linear factors of unknown function.In this paper,the unknown function of the inequality is a two-variable function,the first term of the right hand of the inequality is a nondecreasing and positive function,and the integrand of the second term contains a nonlinear factor of unknown function,and it also contains a nonconstant factor outside the integral sign.Finally,We apply our result to the discussion of boundedness for the initial-boundary value problem of retarded partial differential equation.