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Perturbation theory of eigenvalue problems
Franz Rellich,B. J. Berkowitz +1 more
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The article was published on 1969-01-01 and is currently open access. It has received 600 citations till now. The article focuses on the topics: Inverse iteration & Eigenvalue perturbation.read more
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Factorizations of and extensions to J-unitary rational matrix functions on the unit circle
TL;DR: In this paper, minimal factorizations in the class of J-unitary rational matrix functions on the unit circle and completions of contractive rational matrices were studied in terms of a special realization which does not require any additional properties at zero and at infinity.
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Newton's Method for a Generalized Inverse Eigenvalue Problem
Hua Dai,Peter Lancaster +1 more
TL;DR: In this paper, a generalized inverse eigenvalue problem is proposed which includes the additive, multiplicative and classical inverse Eigenvalue problems as special cases, and a local convergence analysis is given for both the distinct and the multiple eigen value cases.
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Global minimizer of the ground state for two phase conductors in low contrast regime
TL;DR: In this paper, the problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions.
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Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials
Mousomi Bhakta,Roberta Musina +1 more
TL;DR: In this article, the existence, multiplicity and qualitative properties of entire solutions for a non-compact problem related to second-order interpolation inequalities with weights were studied, and the following family of equations Δ 2 u = λ | x | − 4 u + | x − β | u | q − 2 u in R N, where N ≥ 5, q > 2, β = N − q (N − 4 ) / 2 and λ ∈ R is smaller than the Rellich constant.
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Hardy–Rellich inequalities in domains of the Euclidean space
TL;DR: For test functions supported in a domain of the Euclidean space, the authors showed that the Hardy-Rellich inequality holds with sharp constant C 2 = 9/16 if and only if the domain satisfies an exterior sphere condition with certain restriction on the radius of the sphere.