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International Journal of Mathematical Analysis and Applications

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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

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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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