scholarly journals Spectral Properties of Fourth Order Differential Operators with Periodic and Antiperiodic Boundary Conditions

2015 ◽  
Vol 68 (3-4) ◽  
pp. 501-518 ◽  
Author(s):  
Hikmet Gunes ◽  
Nazim B. Kerimov ◽  
Ufuk Kaya
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Spectral Properties ◽  
Differential Operators

Pencils of differential operators containing the eigenvalue parameter in the boundary conditions

2003 ◽  
Vol 133 (4) ◽  
pp. 893-917 ◽  
Author(s):  
Marco Marletta ◽  
Andrei Shkalikov ◽  
Christiane Tretter
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties ◽  
Differential Operators ◽  
Finite Interval ◽  
Linear Operators ◽  
Riesz Bases ◽  
Ordinary Differential Operators ◽  
Associated Functions ◽  
Eigenvalue Parameter

The paper deals with linear pencils N − λP of ordinary differential operators on a finite interval with λ-dependent boundary conditions. Three different problems of this form arising in elasticity and hydrodynamics are considered. So-called linearization pairs (W, T) are constructed for the problems in question. More precisely, functional spaces W densely embedded in L2 and linear operators T acting in W are constructed such that the eigenvalues and the eigen- and associated functions of T coincide with those of the original problems. The spectral properties of the linearized operators T are studied. In particular, it is proved that the eigen- and associated functions of all linearizations (and hence of the corresponding original problems) form Riesz bases in the spaces W and in other spaces which are obtained by interpolation between D(T) and W.

scholarly journals Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2830
Author(s):  
Aigerim Kalybay ◽  
Ryskul Oinarov ◽  
Yaudat Sultanaev
Keyword(s):  
Fourth Order ◽  
Differential Inequality ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Independent Interest ◽  
Compactly Supported ◽  
Compactly Supported Functions

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest.

Spectral properties of ordinary differential operators with involuton

2019 ◽  
Vol 484 (1) ◽  
pp. 12-17 ◽  
Author(s):  
V. E. Vladykina ◽  
A. A. Shkalikov
Keyword(s):  
Boundary Conditions ◽  
Unconditional Basis ◽  
Spectral Properties ◽  
Differential Operators ◽  
Root Functions ◽  
Ordinary Differential Operators ◽  
Normal Boundary ◽  
The Space L2

Let P and Q be ordinary differential operators of order n and m generated by s = max{n; m} boundary conditions on a nite interval [a; b]. We study operators of the form L = JP + Q, where J is the involution operator in the space L2[a; b]. We consider three cases n > m, n < m, and n = m, for which we dene concepts of regular, almost regular, and normal boundary conditions. We announce theorems on unconditional basis and completeness of the root functions of operator L depending on the type of boundary conditions from selected classes.

scholarly journals A Classification of Fourth-Order Dissipative Differential Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Tao Wang ◽  
Ji-jun Ao ◽  
Mei-chun Yang
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Differential Operators ◽  
Dissipative Operators

This paper is devoted to the classification of the fourth-order dissipative differential operators by the boundary conditions. Subject to certain conditions, we determine some nonself-adjoint boundary conditions that generate the fourth-order differential operators to be dissipative. And under certain conditions, we prove that these dissipative operators have no real eigenvalues.

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