A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps

This paper is devoted to the proof of the infinite-dimensional Borsuk-Ulam theorem for odd completely continuous multivalued maps with convex images which are defined on level sets of even functions. The results obtained in the paper are new even for single-valued maps. In the final section some applications of the theorem to analysis and differential equations are discussed. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.