Singular integral inequalities with several nonlinearities and integral equations with singular kernels

We deal with an integral inequality with a power nonlinearity on its left-hand side, n nonlinearities on its right-hand side, and weakly singular kernels. The obtained result is an extension of the Bihari, Henry, Pachpatte, and Pinto inequalities and results obtained by the author. Using these results, we prove sufficient conditions for the existence of global solutions of some nonlinear Volterra integral equations with singular kernels and n nonlinearities. Published in Neliniini Kolyvannya, Vol. 11, No. 1, pp. 71–80, January–March, 2007.