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The topology of the calculus of variations in the large / by L. A. Ljusternik

Auteur principal : Liousternik, Lazar Aronovitch, 1899-1981, AuteurType de document : MonographieCollection : Translations of mathematical monographs, 16Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1966Description : 1 vol. (VII-96 p.) ; 24 cmISBN : 9780821886489.ISSN : 0065-9282.Bibliographie : Bibliogr. p. 95-96.Sujet MSC : 58Axx, Global analysis, analysis on manifolds, General theory of differentiable manifolds
49-01, Calculus of variations and optimal control; optimization, Instructional exposition (textbooks, tutorial papers, etc.)
En-ligne : Zentralblatt | MathSciNet
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Bibliogr. p. 95-96

This paper is chiefly concerned with the results obtained by applying cohomology theory, and in particular the duality principle and the Pontrjagin removing theorem, to the problems of analysis in the large. Chapter I presents the analysis in the large of functions on topological spaces. There are certain applications in chapter II to nonlinear integral equations; but the principal aim is the development of theorems concerning the existence of geodesics in various curve-families on certain manifolds, notably in the family of curves joining two fixed points of a homeomorph of a sphere and the family of closed curves on a homeomorph of an n-sphere. (MathSciNet)

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