共查询到20条相似文献,搜索用时 93 毫秒
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讨论了复空间中强拟凸域上的复Monge-Ampere方程的特征值问题,证明了特征值问题解的存在唯一性,并给出了这个特征值与一类复空间中复Laplace算子的第一特征值的关系,最后利用特征值及特征函数的存在性讨论了一类复Monge-Ampere方程的解的存在性及其分歧. 相似文献
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R. R. Gadyl'shin 《Mathematical Notes》1997,61(4):409-416
The eigenvalue problem for the Laplace operator with the Neumann boundary conditions in a domain that has a thin spike of
finite length is considered for the case in which the limit value is an eigenvalue both for the main body and the spike. The
method of matched asymptotic expansions is used to construct total asymptotics of the eigenvalues of the perturbed problem
and obtain closed formulas for the leading asymptotic terms.
Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 494–502, April, 1997.
Translated by V. E. Nazaikinskii 相似文献
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A. A. Abramov V. I. Ul’yanova L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2009,49(3):474-481
The index of the homogeneous self-adjoint boundary value problem for the Hamiltonian systems of ordinary differential equations is introduced. It is assumed that the system has a nontrivial solution. The relationship between the index of an eigenvalue of the nonlinear eigenvalue problem and the index of the corresponding homogeneous problem is established. Properties of the index of the problem and those of the eigenvalue are examined. 相似文献
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We study the criterion for a new eigenvalue to appear in the linear spectral problem associated with the intermediate long-wave equation. We compute the asymptotic value of the new eigenvalue in the limit of a small potential using a Fourier decomposition method. We compare the results with those for the Schrödinger operator with a radially symmetrical potential. 相似文献
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马冰清 《数学物理学报(B辑英文版)》2012,32(2):745-751
In this article,we study the first two eigenvalues of the higher order buckling problem on a domain in the unit sphere.We obtain an estimate on the second eigenvalue in terms of the first eigenvalue.In... 相似文献
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In this paper, we research the geometric multiplicity of eigenvalues for a nonlocal Sturm–Liouville eigenvalue problem. To this end, we study the uniqueness of solutions for a nonlocal Sturm–Liouville problem under some initial value conditions. 相似文献
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研究了定义在有限区间(0,l)上的具有一般分离型边条件的不定Sturm—Liouville算子的特征函数的振荡问题.利用Prufer变换,给出了上述Sturm-Liouville算子特征值的符号指标的具体形式;得到了特征值的符号指标与Weyl函数以及Prufer角在该特征值处的罗朗展式(泰勒展式)的首项系数的符号之间的关系;最后,在上述两个结果的基础上给出了上述Sturm—Liouville算子的第n个正特征值所对应的特征函数在[0,l]内的零点个数的计算公式. 相似文献
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应用算子特征值准则研究了一类高阶多点边值问题多重正解的存在性,其中非线性项满足Caratheodory条件.将特征值准则应用到n阶m点的非线性边值问题,并证明了微分方程至少三正解的存在性. 相似文献
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本文讨论一类具有特殊结构的Jacobi矩阵的特征值反问题,该问题由描述变截面杆的微分方程离散化得到.我们得到了这个问题有解的一些必要条件,并且通过一些数值例子,说明了L.Lu和K.Michael给出的充分条件和算法在矩阵的阶数高于3的时候是错误的。 相似文献
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Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues
We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics. 相似文献
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Wuqing Ning 《Journal of Mathematical Analysis and Applications》2007,327(2):1396-1419
In this paper, an algorithm is established to reconstruct an eigenvalue problem from the given data satisfying certain conditions. These conditions are proved to be not only necessary but also sufficient for the given data to coincide with the spectral characteristics corresponding to the reconstructed eigenvalue problem. 相似文献
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Toshiaki Yachimura 《Applicable analysis》2013,92(10):1946-1958
In this paper, we consider the asymptotic behavior for the principal eigenvalue of an elliptic operator with piecewise constant coefficients. This problem was first studied by Friedman in 1980. We show how the geometric shape of the interface affects the asymptotic behavior for the principal eigenvalue. This is a refinement of the result by Friedman. 相似文献
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Luka Grubišić 《PAMM》2006,6(1):59-62
We combine abstract eigenvalue/eigenvector estimates (from our earlier work) with a saturation assumption for finite element solution of associated stationary problem to obtain a posteriori estimates of the accuracy of finite element Rayleigh–Ritz approximations. Attention will be payed to the interplay between the accuracy estimate for the finite element method and a strategy for generating an adapted mesh. The obtained results use a preconditioned residuum of Neymeyr and extend his study of eigenvalue approximations with eigenvector estimates. We also prove that this eigenvalue estimator is equivalent to the global error. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Approximation of an Eigenvalue Problem Associated with the Stokes Problem by the Stream Function-Vorticity-Pressure Method 总被引:3,自引:2,他引:1
By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure
method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence
for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of
the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical
experiments are reported.
The first author was supported by China Postdoctoral Sciences Foundation. 相似文献
16.
Adaptive computation of smallest eigenvalues of self‐adjoint elliptic partial differential equations
We consider a new adaptive finite element (AFEM) algorithm for self‐adjoint elliptic PDE eigenvalue problems. In contrast to other approaches we incorporate the inexact solutions of the resulting finite‐dimensional algebraic eigenvalue problems into the adaptation process. In this way we can balance the costs of the adaptive refinement of the mesh with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors, and use these for the adaptation process. We show that it is also possible to restrict to very few iterations of a Krylov subspace solver for the eigenvalue problem on coarse meshes. Several examples are presented to show that this new approach achieves much better complexity than the previous AFEM approaches which assume that the algebraic eigenvalue problem is solved to full accuracy. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction
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Jing An & Jie Shen 《数学研究》2014,47(1):1-20
An important step in estimating the index of refraction of electromagnetic
scattering problems is to compute the associated transmission eigenvalue problem.
We develop in this paper efficient and accurate spectral methods for computing the
transmission eigenvalues associated to the electromagnetic scattering problems. We
present ample numerical results to show that our methods are very effective for computing transmission eigenvalues (particularly for computing the smallest eigenvalue),
and together with the linear sampling method, provide an efficient way to estimate the
index of refraction of a non-absorbing inhomogeneous medium. 相似文献
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A. A. Abramov V. I. Ul’yanova L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2007,47(4):612-619
Properties of the eigenvalues are examined in a nonlinear self-adjoint eigenvalue problem for linear Hamiltonian systems of ordinary differential equations. In particular, it is proved that, under certain assumptions, every eigenvalue is isolated and there exists an eigenvalue with any prescribed index. 相似文献
19.
We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two‐sided estimates for this term in a variety of situations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We study an eignevalue problem with a spectral parameter in a boundary condition. This problem for the Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a half‐space covered by a rigid dock with some apertures (an ice sheet with fishing holes). The dependence of the fundamental eigenvalue on holes' geometry is investigated. We give conditions on a plane region guaranteeing that the fundamental eigenvalue corresponding to this region is larger than the fundamental eigenvalue corresponding to a single circular hole. Examples of regions satisfying these conditions and having the same area as the unit disk are given. New results are also obtained for the problem with a single circular hole. On the other hand, we construct regions for which the fundamental eigenfrequency is larger than the similar frequency for the circular hole of the same area and even as large as one wishes. In the latter examples, the hole regions are either not connected or bounded by a rather complicated curves. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献