On the existence of zero points
The author proves that a continuous function \(F:\mathbb{R}^n\to\mathbb{R}^n\) has at least one zero under one of two smoothness conditions. The constructive proof, based on a homotopy, uses the implicit function theorem and contains a proof of a global implicit function theorem. Numerical methods can be used to follow a solution curve, though no numerical examples are given.
zeros of continuous multivariate functions
scientific article; zbMATH DE number 932158
scientific article