Positive solutions for a class of multi-parameter elliptic systems

摘要

In this paper, we deal with the global existence of positive solutions for a multi-parameter system of second-order elliptic equations with respect to parameters, by using the fixed point index theory in cones, the sub-supersolutions method, Leray-Schauder degree theory and a priori estimates technique. In addition, for the computation of Leray-Schauder degree on the Cartesian product of two ordered intervals, we also establish a result about Leray-Schauder degree on a strict ordered interval induced by a pair of strict lower and upper solutions for a system of second-order elliptic equations.