Approximate method for separation of solutions of nonlinear operator equations (Q1364044)

This article presents a variant of the procedure for separating isolated solutions of nonlinear operator equations \(Tu= 0\) with an operator \(T= I-\overline T\) in a Banach spaces \(E\) on the base of projection methods of sufficiently general type. More exactly, in this procedure it is used a sequence of equations \(T_nu_n= 0\) \((n=1,2,\dots)\) with operators \(T_n= I-\overline T_n\) acting in finite-dimensional subspaces \(E_n\) of \(E\) with a fixed sequence of projection operators \(P_n: E\to E_n\). The basic results are the local theorems on existence, uniqueness and convergence of iterative method of minimal errors, describing, in a constructive manner, balls containing isolated solutions and the global theorem on the one-to-one correspondence between solutions to the original equation \(Tu=0\) and to the approximate equations \(T_nu_n= 0\) for large \(n\).