scholarly journals Plasmonic eigenvalue problem for corners: Limiting absorption principle and absolute continuity in the essential spectrum

2021 ◽  
Vol 145 ◽  
pp. 130-162
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Eigenvalue Problem ◽  
Essential Spectrum ◽  
Absolute Continuity ◽  
Limiting Absorption Principle

Branches of solutions to semilinear biharmonic equations on RN

2006 ◽  
Vol 136 (4) ◽  
pp. 733-758 ◽  
Author(s):  
Yinbin Deng ◽  
Yi Li
Keyword(s):  
Eigenvalue Problem ◽  
Large Class ◽  
Essential Spectrum ◽  
Degree Theory ◽  
Biharmonic Equations ◽  
Linearized Problem ◽  
Image Position ◽  
Fredholm Maps ◽  
Class Of Functions

For a large class of functions f, we consider the nonlinear biharmonic eigenvalue problem We describe the behaviour of the branch of solutions emanating from an eigenvalue of odd multiplicity below the essential spectrum of the linearized problem. The discussion is based on the degree theory for C2 proper Fredholm maps developed by Fitzpatrick, Pejsachowicz and Rabier.

Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations

2019 ◽  
Vol 19 (3) ◽  
pp. 569-593 ◽  
Author(s):  
Rainer Mandel
Keyword(s):  
Fixed Point ◽  
Linear Operator ◽  
Essential Spectrum ◽  
Entire Space ◽  
Limiting Absorption Principle ◽  
Fixed Point Approach

Abstract We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorption principle for the curl-curl operator is proved.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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