Existence tests for solutions of nonlinear equations using Borsuk's theorem

We show how interval arithmetic can be used in connection with Borsuk's theorem to computationally prove the existence of a solution of a system of nonlinear equations. It turns out that this new test, which can be checked computationally in several different ways, is more general than an existing test based on Miranda's theorem in the sense that it is successful for a larger set of situations. A numerical example is included.