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A. Some theorems of implicit functions

A.1 Introduction

Consider the equation

(A.1)

A major role in analysis of (A.1) belongs to the matrix

(A.2)

A.2 Local properties

Suppose that in (Rⁿ × R^m) there exists a point (z⁰, x⁰ such that W(z⁰, x⁰) = 0. Let the derivative of J(z, x) be continuous in a neighborhood (z⁰, x⁰) and

(A.3)

Denote

(A.4)

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