Multiplicity of positive solutions for a (p1,p2)(p1,p2)-Laplacian system and its applications

In this paper, we establish the product formula for the fixed point index on product cone, and the relation between Leray–Schauder degree and a pair of strict lower and upper solutions for a (p1,p2)(p1,p2)-Laplacian system. Based on the product formula of the fixed point index and Leray–Schauder degree theory, we deal with the multiplicity of positive solutions for a class of (p1,p2)(p1,p2)-Laplacian systems. As applications, we prove the global existence of positive solutions for a multi-parameter system of (p1,p2)(p1,p2)-Laplacian equations with respect to parameters.