Geodesic
Asymptotic distribution of eigenvalues of differential equations
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 191-207 
V. N. Tulovskii. Asymptotic distribution of eigenvalues of differential equations. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 191-207. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a2/
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     author = {V. N. Tulovskii},
     title = {Asymptotic distribution of eigenvalues of differential equations},
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     volume = {18},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_2_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper is studied the asymptotic distribution of eigenvalues of the equation $Au=\lambda Bu$, considered in a bounded domain $G\subseteq\mathbf R^n$ with zero boundary conditions. Here $A$ and $B$ are differential operators. Under particular conditions on $A$ and $B$, the asymptotic behavior of the eigenvalues is determined as they tend to $\pm\infty$. Bibliography: 7 titles.

[1] A. Pleijel, “Asymptotic relations for the eigenvalues of certain boundary problems of polar type”, Amer. J. Math., 70:4 (1948), 892–907 | DOI | MR | Zbl

[2] S. Agmon, “On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems”, Comm. Pure Appl. Math., 18:4 (1965), 627–663 | DOI | MR | Zbl

[3] I. M. Glazman, Pryamye metody kachestvennogo spektralnogo analiza singulyarnykh differentsialnykh operatorov, Fizmatgiz, Moskva, 1963 | MR

[4] L. Khermander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, Moskva, 1965 | MR

[5] V. N. Tulovskii, “Raspredelenie sobstvennykh znachenii dlya differentsialnykh operatorov s postoyannymi koeffitsientami”, DAN SSSR, 195:3 (1970), 570–573 | MR | Zbl

[6] D. Fujiwara, “On the asymptotic formula for the Green operators of elliptic operators on compact manifolds”, J. Faculty of Science Univ. Tokyo, Sec. 1, 14:2 (1969), 251–283 | MR

[7] M. Sh. Birman, M. Z. Solomyak, “Ob asimptotike spektra dlya “negladkikh” ellipticheskikh zadach”, Funkts. analiz, 5:1 (1971), 69–70 | MR | Zbl