Global Existence Structure of Parameters for Positive Solutions of a Singular $$(p_1,p_2)$$ ( p 1 , p 2 ) -Laplacian System

Abstract

We study the homogeneous Dirichlet boundary value problem of a singular \((p_1,p_2)\)-Laplacian system with multiparameters. The global structure of multiparameters for existence, nonexistence and multiplicity of positive solutions can be obtained. Proofs are mainly based on the upper and lower solution method, the fixed point index theory in a cone, generalized Picone identity, global continuum theorem and degree arguments. As an application, we can establish the global result of the positive radial and decaying solutions for a class of quasilinear elliptic systems in exterior domains.