scholarly journals On the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 707-721
Author(s):  
Mussakan Muratbekov ◽  
Yerik Bayandiyev
Keyword(s):  
Detailed Analysis ◽  
Unbounded Domain ◽  
Spectral Properties ◽  
Differential Operators ◽  
Elliptic Operators ◽  
Hyperbolic Operator ◽  
Fast Growing ◽  
The Space L2

This paper studies the question of the resolvent existence, as well as, the smoothness of elements from the definition domain (separability) of a class of hyperbolic differential operators defined in an unbounded domain with greatly increasing coefficients after a closure in the space L2(R2). Such a problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that a detailed analysis shows that when studying the spectral properties of differential operators specified in an unbounded domain, the behavior of the coefficients at infinity plays an important role.

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 Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

V.— On the Spectrum of Second Order Partial Differential Operators.

1970 ◽  
Vol 69 (1) ◽  
pp. 77-84
Author(s):  
K. J. Brown ◽  
I. M. Michael
Keyword(s):  
Differential Equations ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Ordinary Differential Operators

SynopsisIn a recent paper, Jyoti Chaudhuri and W. N. Everitt linked the spectral properties of certain second order ordinary differential operators with the analytic properties of the solutions of the corresponding differential equations. This paper considers similar properties of the spectrum of the corresponding partial differential operators.

Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum

1991 ◽  
Vol 44 (1) ◽  
pp. 42-53 ◽  
Author(s):  
Lawrence Barkwell ◽  
Peter Lancaster ◽  
Alexander S. Markus
Keyword(s):  
Hilbert Space ◽  
Real Line ◽  
Spectral Properties ◽  
Eigenvalue Problems ◽  
Real Spectrum ◽  
Hyperbolic Operator ◽  
Quadratic Operator ◽  
Distribution Of Eigenvalues ◽  
Quadratic Eigenvalue Problems ◽  
Quadratic Eigenvalue

AbstractEigenvalue problems for selfadjoint quadratic operator polynomials L(λ) = Iλ2 + Bλ+ C on a Hilbert space H are considered where B, C∈ℒ(H), C >0, and |B| ≥ kI + k-l C for some k >0. It is shown that the spectrum of L(λ) is real. The distribution of eigenvalues on the real line and other spectral properties are also discussed. The arguments rely on the well-known theory of (weakly) hyperbolic operator polynomials.

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