Positive solutions for a class of phi-Laplacian differential systems with multiple parameters

Abstract

In this article, we consider the double eigenvalue problem for a φ-Laplacian differential system. We prove the existence of positive solutions under the φ-super-linear condition by means of the Guo-Krasnosel'skii fixed point theorem and the topological degree. It is shown that there exists a continuous curve splitting ℝ2+ \ {(0, 0)} into disjoint subsets such that systems has at least two, at least one, or no positive solutions according to parameters in different subsets.