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arXiv · 1812.10132

On critical value of the coupling constant in exterior elliptic problems

R. Puri·B. Vainberg
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Abstract

We consider exterior elliptic problems with coefficients stabilizing at infinity and study the critical value $\beta_{cr}$ of the coupling constant (the coefficient at the potential) that separates operators with a discrete spectrum and those without it. The dependence of $\beta_{cr}$ on the boundary condition and on the distance between the boundary and the support of the potential is described. The discrete spectrum of a non-symmetric operator with the FKW boundary condition (that appears in diffusion processes with traps) is also investigated.

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R. Puri, B. Vainberg. 2018-12-25. On critical value of the coupling constant in exterior elliptic problems. https://arxiv.org/abs/1812.10132

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