Electron. J. Diff. Equ., Vol. 2016 (2016), No. 181, pp. 1-8.

Bounded solvability of mixed-type functional differential operators for first order

Bulent Yilmaz, Zameddin I. Ismailov

Abstract:
In this article, we study all boundedly solvable extensions generated by linear mixed-type (forward-backward) functional differential-operator expressions of first order in the Hilbert space of vector-functions on a finite interval. Our main tools are methods of operator theory. Also we study the structure of the spectrum of these extensions.

Submitted May 18, 2016. Published July 10, 2016.
Math Subject Classifications: 47A10, 34K06.
Key Words: Mixed-type functional differential expression; bounded solvable operator; spectrum.

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Bülent Yilmaz
Marmara University, Department of Mathematics
Kadi köy, 34722, Istanbul, Turkey
email: bulentyilmaz@marmara.edu.tr
Zameddin I. Ismailov
Karadeniz Technical University
Department of Mathematics
61080, Trabzon, Turkey
email: zameddin.ismailov@gmail.com

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