In this post, we will see the book The Topology Of The Calculus Of Variations In The Large by L A. Ljusternik.
About the book
In the present paper we investigate the homological properties of functional spaces in connection with the estimation of the number of solutions of the corresponding variational problems. These properties are closely related, on the one hand, to previous work of Moscow mathematicians on topological methods in variational problems, and on the other hand to the investigations of the Moscow topological school on the homology theory of abstract spaces. In a certain sense this paper constitutes a synthesis of both directions of the Moscow topological school.
Translated from the Russian by J. M. Danskin
You can get the book here.
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