EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN
Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 321-332
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For a bounded domain Ω in a complete Riemannian manifold M, we investigate the Dirichlet weighted eigenvalue problem of quadratic polynomial operator Δ2 − aΔ + b of the Laplacian Δ, where a and b are the nonnegative constants. We obtain an inequality for eigenvalues which contains a constant that only depends on the mean curvature of M. It yields an upper bound of the (k + 1)th eigenvalue Λk + 1. As their applications, some inequalities and bounds of eigenvalues on a complete minimal submanifold in a Euclidean space and a unit sphere are obtained.
HEJUN, SUN; XUERONG, QI. EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN. Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 321-332. doi: 10.1017/S0017089510000728
@article{10_1017_S0017089510000728,
author = {HEJUN, SUN and XUERONG, QI},
title = {EIGENVALUE {ESTIMATES} {FOR} {QUADRATIC} {POLYNOMIAL} {OPERATOR} {OF} {THE} {LAPLACIAN}},
journal = {Glasgow mathematical journal},
pages = {321--332},
year = {2011},
volume = {53},
number = {2},
doi = {10.1017/S0017089510000728},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000728/}
}
TY - JOUR AU - HEJUN, SUN AU - XUERONG, QI TI - EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN JO - Glasgow mathematical journal PY - 2011 SP - 321 EP - 332 VL - 53 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000728/ DO - 10.1017/S0017089510000728 ID - 10_1017_S0017089510000728 ER -
%0 Journal Article %A HEJUN, SUN %A XUERONG, QI %T EIGENVALUE ESTIMATES FOR QUADRATIC POLYNOMIAL OPERATOR OF THE LAPLACIAN %J Glasgow mathematical journal %D 2011 %P 321-332 %V 53 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000728/ %R 10.1017/S0017089510000728 %F 10_1017_S0017089510000728
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