Verification of Spectral Analysis of a Self-adjoint Differential Operator “Following Landau and Lifshitz” by Means of Its Green Function

2020 ◽  
Vol 309 (1) ◽  
pp. 299-316
Author(s):  
B. L. Voronov
Keyword(s):  
Spectral Analysis ◽  
Green Function ◽  
Differential Operator

On the spectral properties and positivity of solutionsof a periodic boundary value problemfor a second-order functional differential equation

2020 ◽  
pp. 123-130
Author(s):  
Manuel J. Alves ◽  
Sergey M. Labovskiy
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Spectral Properties ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Functional Differential ◽  
The Green Function

For a functional-differential operator Lu = (1/ρ)(-(pu')' + ∫_0^l▒〖u(s)d_s r(x,s)〗) with symmetry, the completeness and orthogonality of the eigenfunctions is shown. Thepositivity conditions of the Green function of the periodic boundary value problem areobtained.

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.

A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane

2007 ◽  
Vol 14 (1) ◽  
pp. 33-52
Author(s):  
Heinrich Begehr ◽  
Evgenija Gaertner
Keyword(s):  
Dirichlet Problem ◽  
Green Function ◽  
Differential Operator ◽  
Integral Representation ◽  
Half Plane ◽  
Representation Formula ◽  
Higher Order ◽  
Polyharmonic Equation ◽  
Integral Representation Formula ◽  
Upper Half Plane

Abstract On the basis of a higher order integral representation formula related to the polyharmonic differential operator and obtained through a certain polyharmonic Green function, a Dirichlet problem is explicitly solved in the upper half plane.

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