Constant-sign and nodal solutions for singular quasilinear Lane–Emden type systems

We establish the existence of multiple solutions for singular quasilinear Lane–Emden type systems with a precise sign information: two unique solutions of opposite constant sign and a nodal solution with at least components of opposite constant sign. For sign-coupled systems, these components are of changing and synchronized sign. The approach combines sub-supersolutions method and Leray–Schauder topological degree involving perturbation argument.