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Approximation methods for nonlinear problems with application to two-point boundary value problems
Mathematics of Computation
General nonlinear problems in the abstract form F(x) = 0 and corresponding families of approximating problems in the form Ff¡(xn) = 0 are considered (in an appropriate Banach space setting). The relation between "isolation" and "stability" of solutions is briefly studied. The main result shows, essentially, that, if the nonlinear problem has an isolated solution and the approximating family has stable Lipschitz continuous linearizations, then the approximating problem has a stable solutiondoi:10.1090/s0025-5718-1975-0371058-7 fatcat:2qods5pb5ra7jkqypv5xhxo2mm