Some Analytic Techniques for Parametrized Nonlinear Equations and Their Discretizations

摘要

This paper presents general techniques based on the theory of Fredholm operators for analyzing the solutions of parametrized nonlinear equations and their finite-dimensional approximations. In particular, it is shown how to obtain the existence of solution paths, both for a general class of nonlinear equations and for their discretizations, and to develop error estimates. Finally it is also shown that the results include existing results for mildly nonlinear problems. (Author)