An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications

Abstract

A generalization of the classical Leray-Schauder fixed-point theorem based on the infinite-dimensional Borsuk-Ulam-type antipode construction is proposed. A new nonstandard proof of the classical Leray-Schauder fixed-point theorem and a study of the solution manifold of a nonlinear Hamilton-Jacobi-type equation are presented.