Convergence of the Spectral Expansion in the Eigenfunctions of a Fourth-Order Differential Operator

2019 ◽  
Vol 55 (1) ◽  
pp. 8-23
Author(s):  
V. M. Kurbanov ◽  
Kh. R. Godzhaeva
Keyword(s):  
Differential Operator ◽  
Fourth Order ◽  
Spectral Expansion ◽  
Order Differential Operator ◽  
Fourth Order Differential Operator

Jacobi-type polynomials under an indefinite inner product

1981 ◽  
Vol 90 (1-2) ◽  
pp. 147-153 ◽  
Author(s):  
Angelo B. Mingarelli ◽  
Allan M. Krall
Keyword(s):  
Differential Operator ◽  
Fourth Order ◽  
Krein Space ◽  
Inner Product ◽  
Order Differential Operator ◽  
Indefinite Inner Product ◽  
Kreĭn Space ◽  
Image Position ◽  
Fourth Order Differential Operator

SynopsisThe polynomials which are orthogonal with respect towhen α> – 1, M>0 are considered when α<–1 and/or M<0. The Cauchy regularization of 〈·, ·〉 provides orthogonality and generates a Pontrjagin (Krein) space spanned by the polynomials. The polynomials are eigenfunctions associated with a self-adjoint, fourth order differential operator.

scholarly journals Semilinear fourth order boundary value problems

1990 ◽  
Vol 42 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Gerhard Metzen
Keyword(s):  
Maximum Principle ◽  
Differential Operator ◽  
Linear Operator ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Principal Eigenvalue ◽  
Nonlinear Problems ◽  
Order Differential Operator ◽  
Positive Eigenfunction ◽  
Fourth Order Differential Operator

We study a certain linear fourth order differential operator and show the existence of solutions to corresponding nonlinear problems. It will be shown that a maximum principle holds and that under certain conditions the linear operator has a positive principal eigenvalue with corresponding positive eigenfunction.

scholarly journals On Singular Dissipative Fourth-Order Differential Operator in Lim-4 Case

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ekin Uğurlu ◽  
Elgiz Bairamov
Keyword(s):  
Spectral Analysis ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Inverse Operator ◽  
Order Differential Operator ◽  
Associated Functions ◽  
Fourth Order Differential Operator

A singular dissipative fourth-order differential operator in lim-4 case is considered. To investigate the spectral analysis of this operator, it is passed to the inverse operator with the help of Everitt's method. Finally, using Lidskiĭ's theorem, it is proved that the system of all eigen- and associated functions of this operator (also the boundary value problem) is complete.

Sign in / Sign up

Export Citation Format

Share Document