The Mountain-Pass Theorem

David G. Costa
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David G. Costa: University of Nevada, Las Vegas, Department of Mathematical Sciences

Chapter 4 in An Invitation to Variational Methods in Differential Equations, 2007, pp 29-38 from Springer

Abstract: Abstract Roughly speaking, the basic idea behind the so-called minimax method is the following: Find a critical value of a functional ϕ ∈ C1 (X, ℝ) as a minimax (or maximin) value c ∈ ℝ of ϕ over a suitable class A of subsets of X: $$ c = \mathop {\inf }\limits_{A \in \mathcal{A}} \mathop {\sup }\limits_{u \in A} \phi \left( u \right). $$

Keywords: Suitable Class; Bounded Smooth Domain; Bootstrap Argument; Minimax Method; Strict Local Minimum (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-0-8176-4536-6_4

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