Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions

摘要

In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(mu,lambda) in mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface $mathcal{C}$ which separates $mathbb{R}_+^2 imes (0,infty)$ into two regions $mathcal{O}_1$ and $mathcal{O}_2$ such that the problem under consideration has two positive solutions for $( mu,lambda) in mathcal{O}_1,$ at least one positive solution for $( mu,lambda) in mathcal{C}$, and no positive solutions for $( mu,lambda) in mathcal{O}_2.