On the spectrum and scattering for metric graph with fourth order operator

2020 ◽  
Author(s):  
Irina V. Blinova ◽  
Yana M. Van-Yun-Syan ◽  
Igor Y. Popov
Keyword(s):  
Fourth Order ◽  
Order Operator ◽  
Metric Graph

scholarly journals A time-dependent metric graph with a fourth-order operator on the edges

2021 ◽  
pp. 7-7
Author(s):  
I.V. Blinova ◽  
A.S. Gnedash ◽  
I.Y. Popov
Keyword(s):  
Fourth Order ◽  
High Frequency ◽  
Graph Model ◽  
Amplitude Distribution ◽  
Elastic Vibration ◽  
Time Dependent ◽  
Length Variation ◽  
Order Operator ◽  
Metric Graph

The metric graph model is suggested for description of elastic vibration in a network of rods under the assumption that the rod lengths vary in time. A single rod and star-like graph are considered. Influence of the length variation law on the vibration distribution is investigated. For high-frequency length variation one observes a fast transition to high-frequency amplitude distribution

Eigenfunctions of a fourth order operator pencil

2014 ◽  
Author(s):  
Abdizhahan Sarsenbi ◽  
Makhmud Sadybekov
Keyword(s):  
Fourth Order ◽  
Operator Pencil ◽  
Order Operator

The Oscillation of Fourth Order Linear Differential Operators

1975 ◽  
Vol 27 (1) ◽  
pp. 138-145 ◽  
Author(s):  
Roger T. Lewis
Keyword(s):  
Fourth Order ◽  
Differential Operators ◽  
Adjoint Operator ◽  
Oscillatory Behavior ◽  
The Self ◽  
Order Operator ◽  
Order Linear ◽  
Linear Differential Operators ◽  
Even Order ◽  
Linear Differential

Define the self-adjoint operatorwhere r(x) > 0 on (0, ∞) and q and p are real-valued. The coefficient q is assumed to be differentiate on (0, ∞) and r is assumed to be twice differentia t e on (0, ∞).The oscillatory behavior of L4 as well as the general even order operator has been considered by Leigh ton and Nehari [5], Glazman [2], Reid [7], Hinton [3], Barrett [1], Hunt and Namb∞diri [4], Schneider [8], and Lewis [6].

scholarly journals The fourth order strongly noncanonical operators

2018 ◽  
Vol 16 (1) ◽  
pp. 1667-1674 ◽  
Author(s):  
Blanka Baculikova ◽  
Jozef Dzurina
Keyword(s):  
Canonical Form ◽  
Fourth Order ◽  
Canonical Representation ◽  
Order Operator

AbstractIt is shown that the strongly noncanonical fourth order operator$$\begin{array}{} \displaystyle \mathcal {L}\,y=\left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)' \end{array}$$can be written in essentially unique canonical form as$$\begin{array}{} \displaystyle \mathcal {L}\,y = q_4(t)\left(q_3(t)\left(q_2(t)\left(q_1(t)\left(q_0(t)y(t)\right)'\right)'\right)'\right)'. \end{array}$$The canonical representation essentially simplifies examination of the fourth order strongly noncanonical equations$$\begin{array}{} \displaystyle \left(r_3(t)\left(r_2(t)\left(r_1(t)y'(t)\right)'\right)'\right)'+p(t)y(\tau(t))=0. \end{array}$$

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