Introduction

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

Chapter 1 in An Invitation to Variational Methods in Differential Equations, 2007, pp 1-5 from Springer

Abstract: Abstract It is fortunate (for some of us) that many differential equation problems $$ \mathcal{D}\left( u \right) = 0 $$ can be handled by variational techniques, in other words, by considering an associated realvalued function $$ \phi :X \to \mathbb{R}, $$ whose derivative is equal to D(u), and by looking for points of minimum, maximum or minimax (e.g., saddle-like) of ϕ, so that our given problem reads $$ \phi ^\prime \left( u \right) = 0 or D\phi \left( u \right) = \mathcal{D}\left( u \right) = 0. $$

Date: 2007
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DOI: 10.1007/978-0-8176-4536-6_1

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