English

A singular perturbation problem

Analysis of PDEs 2007-05-23 v1

Abstract

Consider the equation s2Δus+q(x)us=f(us)-s^2\Delta u_s+q(x)u_s=f(u_s) in R3\R^3, u()<|u(\infty)|<\infty, s=const>0s=const>0. Under what assumptions on q(x)q(x) and f(u)f(u) can one prove that the solution usu_s exists and lims0us=u(x)\lim_{s\to 0} u_s=u(x), where u(x)u(x) solves the limiting problem q(x)u=f(u)q(x)u=f(u)? These are the questions discussed in the paper.

Keywords

Cite

@article{arxiv.math/0410451,
  title  = {A singular perturbation problem},
  author = {A. G. Ramm},
  journal= {arXiv preprint arXiv:math/0410451},
  year   = {2007}
}