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In a paper from 1960, Felix Browder established a theorem concerning thecontinuation of the fixed points of a family of continuous functions $f_t:X\toX$ depending continuously on a parameter $t\in [0,1]$, where $X$ is a convexand compact subset of $\R^n$. Here, the result is presented for a compactmapping $f:A\times X\to X$ where $X$ is a convex, closed and bounded subset ofan arbitrary normed space and $A$ is an arcwise connected topological space.Applications to nonlinear boundary value problems are given; specifically, weshall present new viewpoints of known results, introduce some novel results andexhibit some open problems.

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