Geodesic
A model of transition from discrete spectrum to continuous one in the singular perturbation theory
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1199-1227
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The spectral problem \begin{gather*} i\varepsilon y''(x)+(x-\lambda)y(x)=0, \\ y(-1)=y(1)=0 \end{gather*} is considered where $\lambda$ is a spectral parameter and $\varepsilon>0$ is a small parameter. Spectrum localization, behavior of eigenfunctions and Green function of this problem are studied by analytical means. 
@article{FPM_1997_3_4_a18,
     author = {S. A. Stepin},
     title = {A~model of transition from discrete spectrum to continuous one in the singular perturbation theory},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1199--1227},
     year = {1997},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/}
}
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S. A. Stepin. A model of transition from discrete spectrum to continuous one in the singular perturbation theory. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1199-1227. http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a18/