Finding more and more solutions of a system of nonlinear equations

摘要

This paper is addressed to an old but difficult topic, viz. how to find more and more solutions of a system of nonlinear equations. We find a transformation by using so-called locally affective functions to transform the original system to a new system, which has not the already found solutions of the original system, but only the unfound solutions, and so we can find a new solution of the original system through finding a solution of the transformed system. We also discuss some likely uses of locally affective functions in the solution of other nonlinear problems.