ON AN EIGENVALUE ASYMPTOTICS FOR A SCHRÖDINGER OPERATOR WITH THE DE GENNES EFFECT ASSOCIATED WITH SUPERCONDUCTIVITY

Junichi Aramaki (Japan)

Received January 15, 2008

Abstract

We study the eigenvalue asymptotics for a Schrödinger operator with a magnetic potential and with the de Gennes effect associated with the superconductivity near critical temperature. When the magnetic potential is depending on a parameter and the parameter tends to zero, we examine the asymptotics of the first eigenvalue and the corresponding eigenfunction. The result improves our previous paper Ando and Aramaki [2] and Pan [21].

Keywords and phrases: eigenvalue problems, the de Gennes effect, superconductivity.