Lectures on the Ekeland variational principle with applications and detours
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Bibliographic Information
Lectures on the Ekeland variational principle with applications and detours
（Lectures on mathematics and physics, Mathematics ; 81）
Published for the Tata Institute of Fundamental Research [by] Springer-Verlag, 1989
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- Other Title
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The Ekeland variational principle
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Note
Bibliography: p. 91-96
"Lectures delivered at the Indian Institute of Science, Bangalore under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics" -- T.p
Description and Table of Contents
Description
Since its publication in 1972, the variational principle of Ekeland has found many applications in different fields of Analysis. Some are very scattered in the literature and therein lies the motivation of these notes. They are intended for the use of students and therefore include several detours through related material. Some readers may be surprised to find a chapter on Nemytskii mappings: however their properties are seldom proved though often referred to and the proofs presented here are more straightforward than those in the standard sources of Krasnoselskii or Vainberg. Two chapters cover applications to (semilinear elliptic) PDE. The central chapter is on BrA(c)zis' proof of the minimax theorems of Ambrosetti and Rabinowitz. To keep the text self-contained, some convex analysis is developed (for the treatment of the duality mapping) and some geometry of Banach spaces. These notes are based on a course given by the author at the Tata Institute in 1987.
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