Potential problems: Smooth case

Abstract

Again, we consider V a reflexive and separable Banach space. Here we shall deal with the case that A : V → V* has the form4.1 A=Φ' for some functional (called a potential) Φ : V → ℝ, having the Gâteaux differential denoted by Φ′ : V → V*. The methods based on the hypothesis (4.1) are called variational methods.