Constant sign and nodal solutions for singular quasilinear elliptic systems

Abstract

We consider singular quasilinear elliptic systems with homogeneous Dirichlet boundary condition. Using Leray-Schauder topological degree, combined with the sub-supersolutions method and suitable truncation arguments, we establish the existence of at least three nontrivial solutions, two of which are of opposite constant sign. The third solution is nodal and exhibits components of at least opposite constant sign. In the case of a sign-coupled system, these components are of changing and synchronized sign.