Speaker: 王林峰 (南通大学数学与统计学院)

Time: Jun 26th Thursday 9:30-11:00
Location: R1310, SIMIS

Abstracts:
Let G=(V,E) be a connected locally finite graph with some volume growth condition and p>1 be a constant. In this report we study the p-Laplace Schrödinger equations on G . We establish two Liouville theorems when the potential function is nonnegative, or decays relatively slowly at infinity. We prove the existence of the nontrivial bounded solution on a homogeneous tree for the case that 1<p<m when the potential function vanishes at infinity, which implies that the condition of the potential function in the Liouville theorem is sharp for the case that 1<p<m , in some sense.