using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

This paper presents a generalization for systems of partial differential equations of Gronwall's classical integral inequality for ordinary differential equations. The proof is by reducing the vector integral inequality to a vector partial differential inequality and then using a vector generalization of Riemann's method to obtain the final inequality. The final inequality involves a matrix fun...

Different types of boundary conditions in industrial numerical simulators involving the discretization of hyperbolic systems are presented. For some of them, one may determine the problem to which the limit of approximate solutions (as the discretization parameters tend to 0) is the unique solution. In turn, this convergence result may suggest other ways to take into account the boundary condit...

Abstract This paper is devoted to prove the existence of positive solutions a second order differential equation with nonhomogeneous Dirichlet conditions given by parameter dependence integral. The studied problem nonlocal perturbation considering homogeneous Dirichlet-type condition at one extreme interval and an integral operator on other one. We obtain expression Green’s function related lin...