A Schrödinger singular perturbation problem

✍ Scribed by A.G. Ramm

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 151 KB
• Volume: 12
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2005.11.002

✦ Synopsis

Consider the equation Àe 2 Du e + q(x)u e = f(u e ) in R 3 , ju(1)j < 1, e = const > 0. Under what assumptions on q(x) and f(u) can one prove that the solution u e exists and lim e!0 u e = u(x), where u(x) solves the limiting problem q(x)u = f(u)? These are the questions discussed in the paper.