Abstract:

In this lecture, we use Brouwer degree to obtain in a simple way a number of results on the existence of zeros and the surjectivity of continuous nonlinear mappings in $n$-dimensional Euclidian space.

The results generalize and unify a number of classical ones, like the Hadamard and the Poincar'e-Miranda theorem, and some of them make use of possibly discontinuous auxiliary mappings and of convexity techniques.

Most of them can be extended to some special classes of mappings in Banach spaces.

Video of the talk.