Related papers: Eigenvalue estimates for the higher order buckling…
In this paper, we investigate the Dirchlet eigenvalue problems of poly-Laplacian with any order and quadratic polynomial operator of the Laplacian. We give some estimates for lower bounds of the sums of their first $k$ eigenvalues which…
This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our…
This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our…
We consider the higher order buckling eigenvalues of the following Dirichlet poly-Laplacian in the unit sphere $(-\Delta)^p u=\Lambda (-\Delta) u$ with order $p(\geq2)$. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the…
In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lam\'e and the Laplacian…
We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the…
In this paper, we give some lower bounds for several eigenvalues. Firstly, we investigate the eigenvalues $\lambda_i$ of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the eigenvalues to general…
In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an $n$-dimensional Euclidean space and obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine…
In this paper, we study eigenvalues of the poly-Laplacian with arbitrary order on a bounded domain in an n-dimensional Euclidean space and obtain a lower bound for eigenvalues, which generalizes the results due to Cheng-Wei [5] and gives an…
In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully get a general…
In this paper, we investigate universal estimates for eigenvalues of a buckling problem. For a bounded domain in a Euclidean space, we give a positive contribution for obtaining a sharp universal inequality for eigenvalues of the buckling…
Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…
In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].
In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity…
We consider the lower order eigenvalues of poly-Laplacian with any order on spherical domains. We obtain universal inequalities for them and show that our results are optimal.
New isoperimetric inequalities for lower order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell-Laplace on bounded domains in a Euclidean space are proven. Some open questions for…
We investigate the lower bound for higher eigenvalues $\lambda_i$ of the poly-Laplace operator on a bounded domain and improve the famous Li-Yau inequality and its related results. Firstly, we consider the low dimensional cases for the…
In this paper, we obtain eigenvalue estimates for a larger class of elliptic differential operators in divergence form on a bounded domain in a complete Riemannian manifold isometrically immersed in Euclidean space. As an application, we…
We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the…
We prove Li-Yau-Kr\"oger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a…