共查询到20条相似文献,搜索用时 15 毫秒
1.
Qing-Ming Cheng Guoxin Wei 《Calculus of Variations and Partial Differential Equations》2011,42(3-4):579-590
In this paper, we study eigenvalues of a clamped plate problem. We obtain a lower bound for eigenvalues, which gives an important improvement of results due to Levine and Protter. 相似文献
2.
Qing-Ming Cheng Hongcang Yang 《Transactions of the American Mathematical Society》2006,358(6):2625-2635
Let be a connected bounded domain in an -dimensional Euclidean space . Assume that are eigenvalues of a clamped plate problem or an eigenvalue problem for the Dirichlet biharmonic operator: Then, we give an upper bound of the -th eigenvalue in terms of the first eigenvalues, which is independent of the domain , that is, we prove the following: Further, a more explicit inequality of eigenvalues is also obtained.
3.
Qiaoling Wang Changyu Xia 《Calculus of Variations and Partial Differential Equations》2011,40(1-2):273-289
In this paper we study eigenvalues of a clamped plate problem on compact domains in complete manifolds. For complete manifolds admitting special functions, we prove universal inequalities for eigenvalues of clamped plate problem independent of the domains of Payne?CPólya?CWeinberger?CYang type. These manifolds include Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifolds and manifolds admitting eigenmaps to a sphere. In the case of warped product manifolds, our result implies a universal inequality on hyperbolic space proved by Cheng?CYang. We also strengthen an inequality for eigenvalues of clamped plate problem on submanifolds in a Euclidean space obtained recently by Cheng, Ichikawa and Mametsuka. 相似文献
4.
Extending the results of Cheng et al. [8], we study eigenvalues of lower order of quadratic polynomial of the Laplacian on a bounded domain in a complete Riemannian manifold and obtain sharp universal inequalities for them. 相似文献
5.
本文研究光滑度量测度空间上带权Paneitz算子的闭特征值问题和带权圆盘振动问题,给出Euclid空间、单位球面、射影空间和一般Riemann流形的n维紧子流形的权重Paneitz箅子和带权圆盘振动问题的前n个特征值上界估计.进一步地,本文给出带权Ricci曲率有界的紧致度量测度空间上带权圆盘振动问题的第一特征值的下界... 相似文献
6.
James R. Kuttler 《Numerische Mathematik》1971,17(3):230-238
Summary A finite-difference scheme is given for the eigenproblem of the clamped plate. The discrete eigenvalues and eigenvectors are shown to converge to the continuous eigenvalues and eigenvectors likeO(h
2) andO (h
2 logh 1/2) respectively.This work, supported by the U.S. Department of the Navy under Contract N 00017-62-C-0604. 相似文献
7.
Fa-en WU~ 《中国科学A辑(英文版)》2007,50(8):1078-1086
Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 < λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang. 相似文献
8.
ESTIMATESOFEIGENVALUESFORUNIFORMLYELLIPTICOPERATOROFSECONDORDERQIANCHUNLIN(钱椿林)CHENZUCHI(陈祖墀)(DepartmentofMathetnatics,Univer... 相似文献
9.
Qing-Ming Cheng Takamichi Ichikawa Shinji Mametsuka 《Calculus of Variations and Partial Differential Equations》2009,36(4):507-523
In this paper we study eigenvalues of the poly-Laplacian with any order on a domain in an n-dimensional unit sphere and obtain estimates for eigenvalues. In particular, the optimal result of Cheng and Yang (Math Ann
331:445–460, 2005) is included in our ones. In order to prove our results, we introduce 2(l + 1) functions a
i
and b
i
, for i = 0, 1, . . . , l and two operators μ and η. First of all, we study properties of functions a
i
and b
i
and the operators μ and η. By making use of these properties and introducing k free constants, we obtain estimates for eigenvalues. 相似文献
10.
J. McLaurin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1968,19(4):676-681
Zusammenfassung Es wird ein Verfahren zur Berechnung von oberen und unteren Schranken für die Eigenwerte einer eingespannten Platte beliebiger Form dargestellt. Die Methode besteht darin, exakte Partikulärlösungen der Plattengleichung (
2
u=u) zu konstruieren, welche die Randbedingungen des Plattenproblems approximativ erfüllen. Der Abstand zwischen dem Eigenwert der Partikulärlösung und einem Eigenwert des Plattenproblems kann dann mit Hilfe eines Lemmas vonMoler undPayne abgeschätzt werden.Als Beispiele wurden die ersten Eigenwerte der quadratischen Platte sowie einiger elliptischer Platten berechnet. Für eine spezielle elliptische Platte sind die ersten vier Eigenwerte angegeben. 相似文献
11.
In this paper, we first establish an abstract inequality for lower order eigenvalues of a self-adjoint operator on a Hilbert space which generalizes and extends the recent results of Cheng et al. (Calc. Var. Partial Differential Equations, 38, 409-416 (2010)). Then, making use of it, we obtain some universal inequalities for lower order eigenvalues of the biharmonic operator on manifolds admitting some speciM functions. Moreover, we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space. 相似文献
12.
It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that |r j | < 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory. 相似文献
13.
In this paper, we investigate eigenvalues of the Dirichlet eigenvalue problem of Laplacian on a bounded domain Ω in an n-dimensional complete Riemannian manifold M. When M is an n-dimensional Euclidean space Rn, the conjecture of Pólya is well known: the kth eigenvalue λk of the Dirichlet eigenvalue problem of Laplacian satisfies
14.
In this paper, we investigate the Dirichlet eigenvalue problems of second order elliptic operators in divergence form on bounded domains of complete Riemannian manifolds. We discuss the cases of submanifolds immersed in a Euclidean space, Riemannian manifolds admitting spherical eigenmaps, and Riemannian manifolds which admit l functions ${f_\alpha : M \longrightarrow \mathbb{R}}$ such that ${\langle \nabla f_\alpha, \nabla f_\beta \rangle = \delta_{\alpha \beta}}$ and Δf α = 0, where ? is the gradient operator. Some inequalities for lower order eigenvalues of these problems are established. As applications of these results, we obtain some universal inequalities for lower order eigenvalues of the Dirichlet Laplacian problem. In particular, the universal inequality for eigenvalues of the Laplacian on a unit sphere is optimal. 相似文献
15.
We study the application,
, where
is the
supremum of positive s such that the problem
admits a solution. Where B 1 is the unit ball in
We show that
is a decreasing function, with
where
is the unique solution of the
problem
.
We also give the explicit solutions of the problem
, when
and show that
. We show that the problem
doesnt admit a solution.
In the end, we give a numerical approximation of
, when
. 相似文献
16.
For an n -dimensional compact submanifold Mn in the Euclidean space RN, we study estimates for eigenvalues of the Paneitz operator on Mn. Our estimates for eigenvalues are sharp. 相似文献
17.
Raffaele Chiappinelli 《Applied mathematics and computation》2010,216(12):3772-3777
We prove upper and lower bounds on the eigenvalues (as the norm of the eigenfunction tends to zero) in bifurcation problems for a class of semilinear elliptic equations in bounded domains of RN. It is shown that these bounds are computable in terms of the eigenvalues of the associated linear equation. 相似文献
18.
Pablo L. De Nápoli 《Journal of Differential Equations》2006,227(1):102-115
In this paper we introduce the generalized eigenvalues of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many continuous eigencurves, which are obtained by variational methods. For the one-dimensional problem, we obtain an hyperbolic type function defining a region which contains all the generalized eigenvalues (variational or not), and the proof is based on a suitable generalization of Lyapunov's inequality for systems of ordinary differential equations. We also obtain a family of curves bounding by above the kth variational eigencurve. 相似文献
19.
This paper gives new bounds for the relationship between the diagonal elements of a square matrix and the corresponding diagonal elements of the matrix inverse, as well as bounds for the eigenvalues of the matrix. The results given here generalize those of Ostrowski and Ky Fan, and have their origin in engineering application. 相似文献
20.
This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The
first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and
the modified nonconforming rotated Q
1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the
enriched modified nonconforming rotated Q
1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space
to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge
at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H
1-and the L
2-norms, and consequently they are locking free.
This work was supported by the National Natural Science Foundation of China (Grant No. 10601003) and National Excellent Doctoral
Dissertation of China (Grant No. 200718) 相似文献