In the beginning was Green

P. AMSTER

Conferencia; Conferencia en Claremont Center for the Mathematical Sciences; 2012

We give a proof of Brouwer's fixed point theorem and related results by means of basic calculus. More specifically, if the mapping is $C^2$, our proof relies only on Green's Theorem. Then, we prove the existence of solutions for some boundary value problems. In particular, we shall give an elementary proof of a theorem by Lazer on the existence of periodic solutions for a second order differential equation.