The Delay-type Nehari Problem

2006 ◽  
pp. 87-108
Keyword(s):  
Nehari Problem

scholarly journals Unexpected Solutions of the Nehari Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
A. Gritsans ◽  
F. Sadyrbaev
Keyword(s):  
Differential Equation ◽  
Multiple Solutions ◽  
Integral Functional ◽  
Characteristic Number ◽  
Nonlinear Ordinary Differential Equation ◽  
Oscillatory Solutions ◽  
Nehari Problem ◽  
Characteristic Numbers ◽  
Regular Shape ◽  
Asymmetric Shape

The Nehari characteristic numbers λn(a,b) are the minimal values of an integral functional associated with a boundary value problem (BVP) for nonlinear ordinary differential equation. In case of multiple solutions of the BVP, the problem of identifying of minimizers arises. It was observed earlier that for nonoscillatory (positive) solutions of BVP those with asymmetric shape can provide the minimal value to a functional. At the same time, an even solution with regular shape is not a minimizer. We show by constructing the example that the same phenomenon can be observed in the Nehari problem for the fifth characteristic number λn(a,b) which is associated with oscillatory solutions of BVP (namely, with those having exactly four zeros in (a,b)).

Frequency domain solution to delay-type Nehari problem

Automatica ◽  
2003 ◽  
Vol 39 (3) ◽  
pp. 499-508 ◽  
Author(s):  
Qing-Chang Zhong
Keyword(s):  
Frequency Domain ◽  
Nehari Problem

Prediction for two processes and the nehari problem

1997 ◽  
Vol 3 (1) ◽  
pp. 43-62 ◽  
Author(s):  
I. Gohberg ◽  
H. J. Landau
Keyword(s):  
Nehari Problem
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