Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors

2012 ◽  
pp. 85-106
Author(s):  
Mikhail Itskov
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Decomposition ◽  
Second Order

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.

Positivity results for a nonlocal elliptic equation

1998 ◽  
Vol 128 (4) ◽  
pp. 697-715 ◽  
Author(s):  
Pedro Freitas ◽  
Guido Sweers
Keyword(s):  
Elliptic Equation ◽  
Eigenvalue Problem ◽  
Parabolic Equations ◽  
Elliptic Systems ◽  
Stationary Solutions ◽  
Second Order ◽  
Real Eigenvalue ◽  
Nonlocal Operator ◽  
Nonlocal Parabolic Equations ◽  
Positive Eigenfunction

In this paper we consider a second-order linear nonlocal elliptic operator on a bounded domain in ℝn (n ≧ 3), and give conditions which ensure that this operator has a positive inverse. This generalises results of Allegretto and Barabanova, where the kernel of the nonlocal operator was taken to be separable. In particular, our results apply to the case where this kernel is the Green's function associated with second-order uniformly elliptic operators, and thus include the case of some linear elliptic systems. We give several other examples. For a specific case which appears when studying the linearisation of nonlocal parabolic equations around stationary solutions, we also consider the associated eigenvalue problem and give conditions which ensure the existence of a positive eigenfunction associated with the smallest real eigenvalue.

scholarly journals Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale

2000 ◽  
Vol 5 (2) ◽  
pp. 91-99 ◽  
Author(s):  
John M. Davis ◽  
Johnny Henderson ◽  
K. Rajendra Prasad ◽  
William Yin
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solution ◽  
Time Scale ◽  
Second Order ◽  
Sigma 1 ◽  
Class Of Functions

We consider the nonlinear second order conjugate eigenvalue problem on a time scale:y ΔΔ(t)+λa(t)f(y(σ(t)))=0,t∈[0,1],y(0)=0=y(σ(1)). Values of the parameterλ(eigenvalues) are determined for which this problem has a positive solution. The methods used here extend recent results by allowing for a broader class of functions fora(t).

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