@article{Prykarpatsky_2008, title={An infinite-dimensional Borsuk-Ulam-type generalization of the Leray-Schauder fixed-point theorem and some applications}, volume={60}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3141}, abstractNote={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.}, number={1}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Prykarpatsky, A. K.}, year={2008}, month={Jan.}, pages={100–106} }