A non-variational approach to the existence of nonzero positive   solutions for elliptic systems
  We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are presented to illustrate the theoretical results. 
Jos\'e \'Angel Cid and Gennaro Infante
math.AP