Existence of positive solutions for systems of nonlinear Sturm-Liouville differential equations with weight functions

Abstract

This article concerns the existence of component-wise positive solutions for systems of nonlinear Sturm-Liouville differential equations with weight functions, in which one nonlinear term is uniformly superlinear or uniformly sublinear, and the other is locally uniformly superlinear or locally uniformly sublinear. As applications, we consider the existence of global component-wise positive solutions to the corresponding nonlinear eigenvalue problem with respect to positive parameters. The discussion is based on the product formula of fixed point index on product cone, the fixed point index theory in cones and Leray-Schauder degree theory.

Keywords

• Positive solution
• nonlinear eigenvalue problem
• fixed point
• strict lower and upper solutions
• Leray-Schauder degree