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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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The well-posedness of a nonlocal multipoint problem for a differential operator equation of second order

Vasyl V. Gorodetskyi / Olga V. Martynyuk
  • Corresponding author
  • Yurii Fedkovych Chernivtsi National University, Kotsyubins’kogo Str. 2, 58000 Chernivtsi, Ukraine
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/ Olesia V. Feduh
Published Online: 2018-07-04 | DOI: https://doi.org/10.1515/gmj-2018-0007

Abstract

We establish the well-posedness of a nonlocal multipoint problem for a second-order evolution equation with respect to a time variable with an operator having a discrete spectrum. A nonlocal condition is considered to be satisfied in a weak sense in the space of formal Fourier series that are identified with continuous linear functionals (generalized elements) on some space connected with the operator.

Keywords: Nonlocal multipoint problem; spaces of generalized elements; operator differential equations; Fourier series; convolution; self-conjugated operators

MSC 2010: 34B10; 46B20

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About the article

Received: 2015-03-27

Revised: 2016-03-22

Accepted: 2016-07-05

Published Online: 2018-07-04


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0007.

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