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

  • A. K. Prykarpatsky


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.
How to Cite
Prykarpatsky, A. K. “An Infinite-Dimensional Borsuk-Ulam-Type Generalization of the Leray-Schauder Fixed-Point Theorem and Some Applications”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, no. 1, Jan. 2008, pp. 100–106,
Research articles