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A simple case within Nash-Moser-Ekeland theory

Milen Ivanov, Nadia Zlateva

Abstract

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

A simple case within Nash-Moser-Ekeland theory

Abstract

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

Paper Structure

This paper contains 3 sections, 3 theorems, 26 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Main result

Key Result

Proposition 1

Let $X=\bigcap_0^\infty (X_n,\|\cdot\|_n)$ be a compactly graded space. Then $C\subset X$ is compact if and only if it is closed and bounded in each norm $\|\cdot\|_n$.

Figures (1)

  • Figure :

Theorems & Definitions (7)

  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Definition 3
  • Theorem 4
  • proof