Gradient method for solving nonlinear discrete and integral equations with difference kernels

The method of potential monotonic operators (called also the Browder–Minty method) is used to prove global theorems on the existence and uniqueness of solutions for discrete and integral equations with difference kernels and odd-power nonlinearities. Using the gradient method (or the steepest descent method), we construct successive approximations that converge to the solutions mentioned with respect to the norm.