Geodesic
Spectrum of an elliptic equation
Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 495-502

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It is shown that the spectrum for the first boundary-value problem for a second-order elliptic equation always lies in the half-plane $\lambda_0\leqslant\mathrm{Re}\,z$, where $\lambda_0$ is the leading eigenvalue to which there corresponds a nonnegative eigenfunction. Apart from $\lambda_0$, there are no other points of the spectrum on the straight line $\mathrm{Re}\,z=\lambda_0$. 
@article{MZM_1970_7_4_a14,
     author = {A. G. Aslanyan and V. B. Lidskii},
     title = {Spectrum of an elliptic equation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {495--502},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a14/}
}
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A. G. Aslanyan; V. B. Lidskii. Spectrum of an elliptic equation. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 495-502. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a14/