Positive solutions of singular elliptic systems with multiple parameters and Caffarelli–Kohn–Nirenberg exponents

Abstract

This paper is concerned with the existence of positive solutions for a class of quasilinear singular elliptic systems with Dirichlet boundary condition. By studying the competition between the Caffarelli–Kohn–Nirenberg exponents, the sign-changing potentials and the nonlinear terms, we establish an interval on the range of multiple parameters over which solutions exist in an appropriate weighted Sobolev space. The arguments rely on the method of weak sub- and super-solutions.