ISSN: 2375-3927
International Journal of Mathematical Analysis and Applications  
Manuscript Information
 
 
Investigations of the Green Function and Discreteness of Spectrum of Higher Order Operator-Differential Equations on Semi-Axis
International Journal of Mathematical Analysis and Applications
Vol.4 , No. 6, Publication Date: Dec. 5, 2017, Page: 52-58
694 Views Since December 5, 2017, 278 Downloads Since Dec. 5, 2017
 
 
Authors
 
[1]    

Gamidulla Aslanov, Department of Functional Analysis, Institute of Mathematics and Mechanics of Azerbaijan National Academy of Sciences, Baku, Azerbaijan.

[2]    

Novrasta Abdullayeva, Department of Differential Equations, Faculty of Natural Sciences, Sumqayit State University, Sumqayit, Azerbaijan.

 
Abstract
 

In the present paper the Green's function and the spectrum of even higher order operator-differential equations are studied. As first the Green's function of the principal part of the equation with frozen coefficients is constructed. By using the Levy method, the integral equation is obtained for the Green's function coefficients. In the Banach spaces of operator valued functions the solution of the obtained integral equations is studied. The uniform estimation of the Green function from which in particular the discreteness of the spectrum is derived.


Keywords
 

Hilbert Space, Banach Space, Operator-Differential Equation, Green's Function, Resolvent, Eigenvalue, Spectrum


Reference
 
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