{
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    "title": "Coercive Solvability of Many-Interval Sturm-Liouville Problems",
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    "abstract": "It is well-known that the Sturm-Liouville type boundary value problems appears in solving many important problems in\r\nphysics. For example, some problems of theory of elasticity in a half-strip ,the problems of theory of vibrations of an elastic cylinder\r\nreduce to investigation of solvability of appropriate boundary value problems for Sturm-Liouville type differential equations. In the\r\nrecent years, the Sturm-Liouville type boundary value problems with additional transmission conditions are investigated by many\r\nmathematical and physical researches . Note that, such type problems is very complicated because boundary value problems with\r\nadditional transmission conditions may be not self-adjoint in the classical Hilbert space L2 and therefore the eigenvalues may be\r\nnot real.\r\nThe main goal of this study is to prove coerciveness of a new class many interval Sturm-Liouville problems with additional\r\ntransmission conditions at the points of interaction. Moreover we shall establish some spectral properties and find asymptotic\r\nbehaviour of the eigenvalues of the problem under consideration.\r\nObserve that this type of problems is studied in the setting of the direct sum of the Hilbert space. We also construct fundamental solutions and discuss some properties of spectrum. ",
    "language": "en",
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    "resource_url": "https://www.set-science.com/a/199fc8db-18ba-4500-bd5a-45933d4701e1",
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    "authors": [
        {
            "public_id": "f1873294-cd0d-4a36-9065-579538e7f611",
            "given": "O. Sh. ",
            "family": "Mukhtarov ",
            "full": "O. Sh.  Mukhtarov ",
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            "email": "omukhtarov@yahoo.com",
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            "affiliations": [
                {
                    "name": "AzerbaijanNational Academy of Sciences ",
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        {
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            "given": "Kadriye",
            "family": "Aydemir",
            "full": "Kadriye Aydemir",
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            "email": "kadriyeaydemr@gmail.com",
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            "affiliations": [
                {
                    "name": "Amasya University",
                    "department": null,
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                    "country_code": null,
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                    "ror_url": null
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            ]
        },
        {
            "public_id": "610512e2-a4c2-451d-9bd3-670b46d606f2",
            "given": "Hayati",
            "family": "Olgar",
            "full": "Hayati Olgar",
            "literal": null,
            "orcid": null,
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            "email": "hayatiolgar@gmail.com",
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            "affiliations": [
                {
                    "name": "Tokat Gaziosmanpaşa University",
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    ],
    "keywords": [
        "Boundary value problem, transmission conditions, Coercive solvability, spectrum, Hilbert space."
    ],
    "translations": [
        {
            "language": "en",
            "title": "Coercive Solvability of Many-Interval Sturm-Liouville Problems",
            "abstract": "It is well-known that the Sturm-Liouville type boundary value problems appears in solving many important problems in\r\nphysics. For example, some problems of theory of elasticity in a half-strip ,the problems of theory of vibrations of an elastic cylinder\r\nreduce to investigation of solvability of appropriate boundary value problems for Sturm-Liouville type differential equations. In the\r\nrecent years, the Sturm-Liouville type boundary value problems with additional transmission conditions are investigated by many\r\nmathematical and physical researches . Note that, such type problems is very complicated because boundary value problems with\r\nadditional transmission conditions may be not self-adjoint in the classical Hilbert space L2 and therefore the eigenvalues may be\r\nnot real.\r\nThe main goal of this study is to prove coerciveness of a new class many interval Sturm-Liouville problems with additional\r\ntransmission conditions at the points of interaction. Moreover we shall establish some spectral properties and find asymptotic\r\nbehaviour of the eigenvalues of the problem under consideration.\r\nObserve that this type of problems is studied in the setting of the direct sum of the Hilbert space. We also construct fundamental solutions and discuss some properties of spectrum. \r\n",
            "keywords": [
                "Boundary value problem, transmission conditions, Coercive solvability, spectrum, Hilbert space."
            ]
        }
    ],
    "subjects": [],
    "subject_names": [],
    "published_date": "2018-12-31",
    "published_year": "2018",
    "received_date": null,
    "accepted_date": null,
    "volume": "3",
    "issue": null,
    "page_first": "1103",
    "page_last": "1106",
    "article_number": null,
    "conference": {
        "short_name": "ISAS2018-Winter",
        "full_title": "2nd International Symposium on Innovative Approaches in Scientific Studies",
        "name": "2nd International Symposium on Innovative Approaches in Scientific Studies",
        "acronym": "ISAS2018-Winter",
        "location": "Samsun, Türkiye",
        "start_date": "2018-11-30",
        "end_date": null,
        "public_id": "b8a703cc-09f7-4d5b-ae60-eb31a1050720"
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    "proceedings": {
        "title": "2nd International Symposium on Innovative Approaches in Scientific Studies",
        "series_title": "Setsci conference indexing system",
        "publisher": "SET Technology",
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        "eisbn": null,
        "issn": "2618-6446",
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        "doi": null,
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        "slug": "setsci-volume-3-2018-legacy-39",
        "public_id": "641f522e-9cf0-4c89-be17-c6037f3d1bca",
        "url": "https://www.set-science.com/p/setsci-volume-3-2018-legacy-39"
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        "name": "CC BY 4.0",
        "url": "https://creativecommons.org/licenses/by/4.0/",
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    "copyright": {
        "holder": "SET Technology",
        "year": "2018"
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    "references": [
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