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- W2734720412 abstract "In this paper, we investigate the boundary value problem of the following operator $$left{begin{array}{l}Delta^{2}u-arm divit Anabla{u}+Vu=rholambda{u} hbox{in} rmOmega, u|_{partial Omega}=frac{partial u}{partial v}|_{partial Omega}=0, end{array}right.$$ where $Omega$ is a bounded domain in an $n$-dimensional complete Riemannian manifold $M^n$, $A$ is a positive semidefinite symmetric (1,1)-tensor on $M^n$, $V$ is a non-negative continuous function on $Omega$, $v$ denotes the outwards unit normal vector field of $partial Omega$ and $rho$ is a weight function which is positive and continuous on $Omega$. By the Rayleigh-Ritz inequality, we obtain universal inequalities for the eigenvalues of these operators on bounded domain of complete manifolds isometrically immersed in a Euclidean space, and of complete manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to a sphere." @default.
- W2734720412 created "2017-07-21" @default.
- W2734720412 creator A5018542785 @default.
- W2734720412 date "2017-06-01" @default.
- W2734720412 modified "2023-10-17" @default.
- W2734720412 title "Universal inequalities for eigenvalues of a class of operators on Riemannian manifold" @default.
- W2734720412 doi "https://doi.org/10.2996/kmj/1499846596" @default.
- W2734720412 hasPublicationYear "2017" @default.
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