A topological approach to the existence and multiplicity of positive   solutions of $(p,q)$-Laplacian systems
  In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory. 
Gennaro Infante, Mateusz Maciejewski and Radu Precup
math.AP