共查询到20条相似文献,搜索用时 31 毫秒
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本文研究了一类具有特殊转移条件且两个边界条件中带有特征参数的四阶微分算子的自共轭性问题.建立了一个与其相关的新的空间H,将上述问题的研究转化为对此空间中一个线性算子A的研究. 相似文献
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We consider the appearance of discrete spectrum in spectralgaps of magnetic Schrödinger operators with electric backgroundfield under strong, localised perturbations. We show that forcompactly supported perturbations the asymptotics of the countingfunction of the occurring eigenvalues in the limit of a strongperturbation does not depend on the magnetic field nor on thebackground field. 相似文献
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M. Denche 《Results in Mathematics》1999,35(3-4):216-227
In the present paper, we first establish a coerciveness estimate with respect to both the space variable and the spectral parameter of a boundary-value problem for an operator differential equation with nonlocal boundary conditions containing the spectral parameter. Then, using the coerciveness estimate, we prove that the operator generated by this problem is a Fredholm, and, moreover is an isomorphism between appropriate spaces. Finally, the results obtained are applied to a class of non local problems for a quasi-elliptic partial differential equation. 相似文献
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Doklady Mathematics - The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is... 相似文献
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Günter Berger 《Mathematische Nachrichten》2000,220(1):11-32
Spectral properties of strongly elliptic operators of second order on bounded snowflake domains without W12–extension property are investigated. We prove that the operators have a pure point spectrum and the asymptotic eigenvalue distributions for the counting function N(λ) are of Weyl type. It is shown that the remainder estimate of N(λ) for Dirichlet and Neumann boundary conditions depends on the inner and outer Minkowski dimension of the boundary ∂Ω, respectively. 相似文献
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A second-order differential operator self-adjoint with respect to an indefinite metric on the circle is considered. The spectral resolution of this operator is found. The hypergeometric function is used in the computation of the Plancherel measure. 相似文献
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Günter Berger 《Mathematische Nachrichten》1993,161(1):345-360
The paper deals with spectral properties of elliptic operators of second order in irregular unbounded domains with cusps. The eigenvalue asymptotic of the operator with Neumann boundary conditions is proved. The eigenvalue asymptotic in these domains is different from that with Dirichlet boundary conditions. 相似文献
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Hynek Kovařík 《Journal of Geometric Analysis》2014,24(3):1509-1525
In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we establish two-sided estimates on the lowest eigenvalues in terms of the inradius and of the boundary conditions. 相似文献
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Transformations Between Sturm-Liouville Problems with Eigenvalue Dependent and Independent Boundary Conditions 总被引:1,自引:0,他引:1
Binding Paul A.; Browne Patrick J.; Watson Bruce A. 《Bulletin London Mathematical Society》2001,33(6):749-757
Explicit relationships are given connecting almostisospectral Sturm-Liouville problems with eigen-value dependent,and independent, boundary conditions, respectively. Applicationis made to various direct and inverse spectral questions. 2000Mathematics Subject Classification 34B24, 34L05, 47E05. 相似文献
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We establish differential properties of generalized solutions of multipoint boundary-value problems for ordinary differential equations. 相似文献
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研究了一类具有有限谱的带有谱参数边界条件的四阶微分方程边值问题及其矩阵表示,证明了对任意正整数m,所考虑的问题至多有2m+6个特征值,进一步给出这类带有谱参数边条件的四阶边值问题与一类矩阵特征值问题之间在具有相同特征值的意义下是等价的. 相似文献
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研究有限区间内一类边界条件含特征参数的不连续奇异Sturm-Liouville问题.利用函数论和算子理论的方法,证明该问题的自伴性,得到其特征值的相关性质,基本解及其特征值的渐近公式. 相似文献
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For Sturm-Liouville problems on [a, ) with a regular -dependentboundary condition at a, and the limit point case at , a techniqueof W. N. Everitt [1] is employed to obtain asymptotic formulaefor the associated m()-functions on rays and lines in the complex-plane. The method relies on asymptotic formulae for solutionsof the initial value problem for u'+qu = u, as || ,which the author has given in [4]. For the case of the regularleft endpoint, the asymptotic formulae on vertical lines sufficeto provide a direct proof of the formula for the total variationof the associated spectral function, a question which the authorhad raised in [3; Remark 5.2]. 相似文献
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Mathematical Notes - 相似文献
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We show that a class of regular self-adjoint fourth order boundary value problems (BVPs) is equivalent to a certain class of matrix problems. Conversely, for any given matrix problem in this class, there exist fourth order self-adjoint BVPs which are equivalent to the given matrix problem. Equivalent here means that they have exactly the same spectrum. 相似文献