Abstract. In this paper we consider the existence of nonzero
solutions of an undecoupling elliptic system with zero Dirichlet condition.
We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions
and we give applications to biharmonic equations and the scalar case.
AMSclassification. Primary 35J55; Secondary 47H11
Keywords. Elliptic system, Leray-Schauder degree, maximum principle.