Global and asymptotic behaviors of bifurcation curves of one-dimensional nonlocal elliptic equations

Abstract

We study the one-dimensional nonlocal elliptic equation−(∫01|u(x)|pdx+b)qu″(x)=λu(x)p,x∈I:=(0,1),u(x)>0,x∈I,u(0)=u(1)=0, where b≥0,p≥1,q>1−1p are given constants and λ>0 is a bifurcation parameter. We establish the global behavior of bifurcation curves and precise asymptotic formulas for uλ(x) as λ→∞.

Topics & Concepts