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Nonlinear eigenvalue problems with specified eigenvalues [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed ...
Karow, Michael +2 more
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Localization theorems for nonlinear eigenvalue problems [PDF]
SIAM Review, 2013 Let $T : \Omega \rightarrow \bbC^{n \times n}$ be a matrix-valued function that is analytic on some simply-connected domain $\Omega \subset \bbC$. A point $\lambda \in \Omega$ is an eigenvalue if the matrix $T(\lambda)$ is singular.
Bindel, David, Hood, Amanda
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Nonlinear eigenvalue problems [PDF]
Bulletin of the Australian Mathematical Society, 1975 The object of this paper is to prove two new results on the nature of the spectrum of a class of nonlinear elliptic eigenvalue problems. In the first case, sufficient conditions are given for which the spectrum is bounded and, in the second case, conditions are given for which the spectrum is open.
Fradkin, L. Ju., Wake, G. C.
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Poiseuille Flow with Couple Stresses Effect and No-slip Boundary Conditions [PDF]
Journal of Applied and Computational Mechanics, 2020 In this paper, the problem of Poiseuille flow with couple stresses effect in a fluid layer using the linear instability and nonlinear stability theories is analyzed.
Akil J. Harfash, Ghazi A. Meften
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Nonlinear eigenvalue problems [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 15 pages, 8 ...
Fring, A., Bender, C., Komijani, J.
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Results in Applied Mathematics, 2020 The interior elastic transmission eigenvalue problem, arising from the inverse scattering theory of non-homogeneous elastic media, is nonlinear, non-self-adjoint and of fourth order.
Xia Ji, Peijun Li, Jiguang Sun
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Nonlinear elliptic equation with nonlocal integral boundary condition depending on two parameters
Mathematical Modelling and Analysis, 2022 In this paper, the two-dimensional nonlinear elliptic equation with the boundary integral condition depending on two parameters is solved by finite difference method.
Kristina Pupalaigė +2 more
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Nonlinearizing Two-parameter Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications, 2021 We investigate a technique to transform a linear two-parameter eigenvalue problem, into a nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of the equations in the two-parameter eigenvalue problem, by considering it as a (standard) generalized eigenvalue problem. We characterize the equivalence between the original
Emil Ringh, Elias Jarlebring
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Asymptotic Behavior of Solution to Nonlinear Eigenvalue Problem
Mathematics, 2020 We study the following nonlinear eigenvalue problem: −u″(t)=λf(u(t)),u(t)>0,t∈I:=(−1,1),u(±1)=0, where f(u)=log(1+u) and λ>0 is a parameter. Then λ is a continuous function of α>0, where α is the maximum norm α=∥uλ∥∞ of the solution uλ associated with λ.
Tetsutaro Shibata
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Comment on ‘Nonlinear eigenvalue problems’ [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 The asymptotic behaviour of solutions to y'(x)=cos[πxy(x)] was investigated by Bender et al (2014 J. Phys. A: Math. Theor. 47 235204). They found, for example, a relation between the initial value y(0)=a and the number of maxima that the solution exhibited.
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