Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation

Abstract

In this article, we study the bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we prove the existence of multiple positive solutions and show the uniqueness of positive solutions for a bifurcation parameter in a certain range.

Keywords

• Bifurcation
• positive solution
• (p,q)-Laplace equation
• time map
• multiple solutions