Special Session 23: Topological and Variational Methods for Differential Equations

A Topological Approach to Nonlocal Elliptic Partial Differential Equations on an Annulus

Christopher Goodrich
UNSW Sydney
USA
Co-Author(s):    
Abstract:
I will consider the boundary value problem $$-a\left(\int_{\Omega}|u|^q\ d\bm{s}\right)\Delta u(\bm{x})=\lambda g\big(u(\bm{x})\big)\text{, }\bm{x}\in\Omega,$$ where $\Omega$ is an annular region in $\mathbb{R}^{n}$ for $n\ge3$. The one-dimensional case ($n=1$), which leads to the problem $$-a\left(\int_0^1|u|^q\ ds\right)u``(t)=\lambda f\big(t,u(t)\big)\text{, }0