FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 4, PAGES 1199-1227

A model of transition from discrete spectrum to continuous one in the singular perturbation theory

S. A. Stepin

Abstract

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The spectral problem

$$ iey^''(x) + (x - l)y(x) = 0,
y(-1) = y(1) = 0

is considered where $$l is a spectral parameter and $$e > 0 is a small parameter. Spectrum localization, behavior of eigenfunctions and Green function of this problem are studied by analytical means.

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Location: http://mech.math.msu.su/~fpm/eng/97/974/97419h.htm
Last modified: January 27, 2000