On some new weakly singular Volterra integral inequalities with maxima and their applications

*Correspondence: [email protected] Department of Mathematics, Sichuan University for Nationalities, Kangding, Sichuan 626001, P.R. China Abstract In this paper, we consider a general form of nonlinear integral inequalities with the unknown function composed with a given function on the left hand side, more than one distinct nonlinear integrals on its right-hand side, and weakly singular kernels, and involving maxima of unknown function. Requiring neither monotonicity nor separability of given functions, we apply monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply the obtained result to a boundary value problem of integro-differential equations with maxima for uniqueness.