Special Session 37: Nonlinear elliptic problems in geometry and physics

Existence results of positive solutions to semi-linear elliptic problems on metric graphs

Masataka Shibata
Meijo University
Japan
Co-Author(s):    
Abstract:
We consider elliptic equations $- \epsilon^2 u'' + u= u^p$ on compact metric graphs, where $p>1$ is a given constant and $\epsilon$ is a positive parameter. We focus on the multiplicity of positive solutions for sufficiently small $\epsilon$ and introduce some results about the existence of positive solutions.