Asymptotic profile of a least-energy solution to a nonlinear elliptic equation in nonlinear optics

Abstract

We consider a least-energy solution to a nonlinear elliptic equation arising in a nonlinear optics model. The equation is linear in a given bounded domain D and nonlinear in R N \ D. We consider a singular limiting problem to obtain a relation between a location of a spiky solution and a geometry of D.