{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:44:51Z","timestamp":1760143491767,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T00:00:00Z","timestamp":1707436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP 14869558","AP 19678089"],"award-info":[{"award-number":["AP 14869558","AP 19678089"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, the symmetric operator L corresponding to the boundary value problem is represented as the difference of two commuting operators A and\u00a0B.\u00a0The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required.<\/jats:p>","DOI":"10.3390\/sym16020210","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T08:12:03Z","timestamp":1707466323000},"page":"210","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Criteria for the Uniqueness of a Solution to a Differential-Operator Equation with Non-Degenerate Conditions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5504-6362","authenticated-orcid":false,"given":"Baltabek","family":"Kanguzhin","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"},{"name":"Department of Mathematics, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0784-5183","authenticated-orcid":false,"given":"Bakytbek","family":"Koshanov","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan"},{"name":"Department of Mathematical and Computer Modeling, International University of Information Technologies, Almaty 050040, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,9]]},"reference":[{"key":"ref_1","unstructured":"Fridman, A. 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Commun."},{"key":"ref_15","first-page":"317","article-title":"Mathematical Methods in Quantum Mechanics with Applications to Schrodinger Operators","volume":"157","author":"Teschl","year":"2014","journal-title":"Grad. Stud. Math."},{"key":"ref_16","first-page":"14","article-title":"Sturm-Liouville operators and applications","volume":"373","author":"Marchenko","year":"2011","journal-title":"Am. Math. Soc."},{"key":"ref_17","unstructured":"Naimark, M. (1969). Linear Differential Operators, Nauka."},{"key":"ref_18","unstructured":"Lions, J.L., and Magenes, E. (1969). Problemes aux Limites non Homogenes et Applications, Dunod."},{"key":"ref_19","first-page":"6","article-title":"Uniqueness of the solution of a time-nonlocal problem for a high-order differential-operator equation l(\u00b7) \u2212 A with a shifted wave operator A","volume":"63","author":"Kanguzhin","year":"2022","journal-title":"Sib. Math. J."},{"key":"ref_20","first-page":"6","article-title":"Uniqueness Criteria for Solving a Time Nonlocal Problem for a High-Order Differential Operator Equation l(\u00b7) \u2212 A with a Wave Operator with Displacement","volume":"14","author":"Kanguzhin","year":"2022","journal-title":"Simmetry"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1134\/S0012266123010019","article-title":"Criteria for the uniqueness of a solution to a time-nonlocal problem for an operator-differential equation l(\u00b7) \u2212 A with the Tricomi operator A","volume":"59","author":"Kanguzhin","year":"2023","journal-title":"Differ. 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