On a theorem by Browder and its application to nonlinear boundary value problems

Abstract

AbstractIn a paper from 1960, Felix Browder established a theorem concerning the continuation of the fixed points of a family of continuous functions depending continuously on a parameter , where is a convex and compact subset of . Here, the result is presented for a compact mapping where is a convex, closed, and bounded subset of an arbitrary normed space and is an arcwise connected topological space. Applications to nonlinear boundary value problems are given; specifically, we shall present new viewpoints of known results, introduce some novel results, and exhibit some open problems.