Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 01, pp. 1-13.

Title: Positive solutions for a class of phi-Laplacian differential systems with multiple parameters
       
Authors: Xiaozhu Yu   (China Univ. of Geosciences, Beijing, China)
         Shiwen Jing  (China Univ. of Geosciences, Beijing, China)
         Hairong Lian (China Univ. of Geosciences, Beijing, China)

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 
$\mathbb{R}_+^2\backslash\{(0,0)\}$
into disjoint subsets such that systems has at least two, at least one, or no positive
solutions according to parameters in different subsets.


Submitted August 27, 2021. Published January 05, 2022.
Math Subject Classifications: 34B16, 34L15.
Key Words: phi-Laplacian differential systems; eigenvalue; fixed point theorem;
           degree theory; positive solution.