Литература
Кальменов Т.Ш., Шалданбаев А.Ш., Ахметова С.Т. К спектральной теории уравнений с отклоняющимися аргументами. Математический журнал, Алматы 2004, т 4, №3 (13), 41-48с.
Ахиезер Н.И., Глазман И.М. Теория линейных операторов в гильбертовом пространстве. – М.: Наука, 1966.-543с.
Гохберг Н.Ц., Крейн М.Г. Введение в теорию линейных несамосопряженных операторов в гильбертовом пространстве.- М.: Наука, 1965.-448с.
Бари Н.К. О базисах в гильбертовом пространстве. //ДАН, 54(1946), 383-386с.
УДК 517.929
О ЗАДАЧЕ КОШИ ДЛЯ УРАВНЕНИЯ ПЕРВОГО ПОРЯДКА С ОТКЛОНЯЮЩИМСЯ АРГУМЕНТОМ
Ахметов Р.
Южно – Казахстанский Государственный Университет им. М.Ауезова, г.Шымкент
Научный руководитель – д.ф.-м.н., доцент Шалданбаев А.Ш.
Введение
В приложениях часто встречается задача на собственные значения в более общей
форме
![](data:image/png;base64,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) , (1.1)
где и - операторы в или, в более общем случае, операторы из в другое банахово пространство .
Существует несколько различных подходов к обобщенной задаче на собственные значения. Например, если существует оператор ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAALCAYAAABPhbxiAAAACXBIWXMAAA7cAAAORgFzG3QkAAABDUlEQVR4nGP59+/ffwYyAAuxCj88ucywZPpchmfSgQyO2Q4IjX8+P2NoyYllsKjfx+Au94XhyM6dDA/efQXLicobMNiaKjHY2RowrL/5l+Evso03jx1k+MvPw/Dk9QcGBjkWBmUtfQbRn7/Bcpy8ogzcnNwMosJ8qE59d/80w80/igzeZvIMJ79/Z2BkkWCQUlRmkEJy6vc3dxlWb9nNcO8JM8Orqr0MLP//fGVYt3gOw5lX3Az/Xl5kEAx7C1QmgeFHThFlhrzG6QgbT67qZ3gln8Awo86S4dyKWob+h4+AwtoEA4vl/R85BhNNMQaQzT9FTBgCeQWJCmUWz7g4OMfSxZ8oTWCNRKuklkYA5CJVKDzbb8AAAAAASUVORK5CYII=) , то уравнение (1.1) можно переписать в виде
![](data:image/png;base64,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) . (1.2)
Поскольку ![](data:image/png;base64,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) - оператор в , то мы свели задачу (1.1) к обычной задаче на собственные значения. Уравнение(1.1) можно переписать также в виде
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAALCAYAAAAz46C7AAAACXBIWXMAAA7OAAAORgE9Bde0AAAEvUlEQVR4nO2WeUxUVxTGf+AgMDMyCIhsU2SQwgwii4OK0JawNEKwVKwNxqJtbU2sMTYm1TQ1atLG/qFN7Rpbl6a1dI01ldhKFRcWRRQXIChakCkgAgNDHRyWAaZvHvQBSTEaGtsmPcl77757z/nOd79zz8uTDQ4O2vjf7mmyiQR33Czjg51f4JW2hrUZ4X8Xp3+dyQo+3Ma3NR20VFYwPWI2hj4l+Z9sFxetXU28tW4VT2zNJ0lt4kTecZrM3eKaT9h8EnRhxMeEUG8bmDARq+k3vt73PqWDc/l447MTxrsfszSW8tqWvazb8Slhno7j+snkofPYlubBmzu82bx9A7WVF6XFa8WF9LvJaTYaYYYnIRGR+FmHBFFMnYarwg1PlYL6YX/7Ro9dbmRBbATN1y9h841B56u8L8JO7l4seXEt7XtK+L3PhrzvFsfOG0SsxqorOAZGjcHqar5KfnUXS5LCKT51kSB9DP5T5A8kUlFJBc4u3ZjMveBhk3B8Jlmoae5CFzxjSKS41DTqTu/FLWyWmMR/QYK4YG+lX23BLNSrudrZK86pg0PGJLH75J09R7OjIIxeQ2vVBY7+nI+z01pMl4tpEYTVCW1o99t/4EdMvSOx3po4XnohA8WfBXSQU1dVQHWzBZnMgZLT5/jpSD5K5xxuXThNu3GqiCUWQzjhBWfPk3vyKlEe/ZSXnqLf51H8tYJINgvf7HqbSuPgKKYqVm/cRKBq5PPbUHaYQU06EQ0X6LX2UnemlLKjBzFM0RLX8wvflyvYun5YJPut6mIdwREJI5hCokMH9nOubTIDtytRP2f+y0p4BM1lyztzpXeddxLlBcVoQjUYO8OYFacdojhdw5MZT4vjXuEgOk8CR8X0MVid107weV4N3mGJonCJSUmUHD+JOiQK145WYhJDJV8npT/JCZGcvdLOjNAQdE3thGu8JLFjUzLRWW1SLvtT7mLvgKGKDFiM7Nn3JWbVGW7UNLEq2UJi/EJkxwvR+TtRe7QB3/BMKZ9MrMqlahIT3SSByr57j9bAHN7dHE9F7hvsMzQICyMkxzOHvgYMN50oLcjFZ9YiYof7vKfHjMFQx4CD88hGPZ0JCnlEHNs5fPTZIZaufJmiw0UcKaogQ+9AS71cwPpKwMpgjksju3cWkbMhRxSxp6MRU4uNHw7mEp6yimnOjhJ/U2sDjWaHUcxcCdAJp8iefqCTY/u3E7B0F6uT3dm97VUMLR1CnDvXW2vRlheSV1KINkVLrUnJTI82ZL3mO8xPT0c9ZbIEaewLQK/zxtXazYDPHNL8VNwVTq9i/G/bED+XYLKeiUYZnYJ+ppc0r/AIYtHioHHjuk2tPL7ydeZp3XG53YLV1w/bZBmZi6NQ6VNFLEvTSerbRtpFFRBFZnwH4U+tGNNG9pOkT16MfrxcXXe4OzWayEAnBrot+EYmIBcKZo97Piubhn4Va17ZRLXJFbW1nq5rlciUvlqWZWvHJEnPyZFeE1Kz7q3MaBNiE5dm37//sLmpo3lseByZkirNJ2cvk8Ymo5L1W5ZLhbK33BDPB/vNc1U9wpLlI/vLzFohjUeLa1fkVsV52m54T+w/6WGaf2TsQ8/pNztWvP4zIv2T9gfCEbVmyL/PSQAAAABJRU5ErkJggg==) (1.3)
и снова мы приходим к обычной задаче на собственные значения, на сей раз для оператора ![](data:image/png;base64,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) , действующего в пространстве .
Можно сделать преобразование к более симметричному виду
![](data:image/png;base64,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) (1.4)
Этот прием удобен, когда и - симметричные операторы в гильбертовом пространстве. Конечно, в (1.4) предполагается, что ![](data:image/png;base64,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) .
В каждом из приведенных выше приемов есть элемент произвола. Не один из них не является более предпочтительным, чем другие. Кроме того, не ясны связи между первоначальной задачей на собственные значения и спектрами операторов ![](data:image/png;base64,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) и ![](data:image/png;base64,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) . Конечно, каждое собственное значение задачи (1.1) является в то время собственным значением задачи (1.2) или (1.3) и каждый собственный вектор для уравнения (1.1) соответствует собственному задачи (1.2) или (1.3). Однако, неясно, что следует понимать под изолированием собственным значением задачи (1.1) или под алгебраической кратностью такого собственного значения; может случиться, что число 𝜆 является изолированным собственным значением для (1.2) и не является таковым для (1.3), и наоборот.
К более узкому классу относится следующая задача
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAALCAYAAAAX+i97AAAACXBIWXMAAA6+AAAORgE2J9p1AAAC1ElEQVR4nM2Ta0hTYRjHf+Z0TTPN1NxkTRbZjs45jNS1EitLmkheKiOMiu5BNwIz+5RQUEF0g8ggiC5Y+SEoK7HsYmYWpkmShqR4WUYmJC7TdKedWSu7kX2pP5zDe573eZ739/7P+8rsdrvIfyTZtf07uGztprniKeooAx1eoRQdyvnrhgO9nRSdPc6ZWg8Kj+ZgH7SRuziNd4nbObbcwNbUdMJzC9iQoPk5kF/cXPao5OwSdeTlLaOlpYOe1ifceWnHMkOgqvguHroYjNqAP9uhIoDkrA10HCmka9ANP0dMFaEhJcnkGNkQdWYyZ4ZSffsCbprZCOM/crO4BlOGBX93Edn0+ETqbxxGZYgk2NefoHA5D8sruJ5/EpVwgrdvXiBqpmF0tJN2e/HIPmrfDLgA3D2CWJ+zjRDF1z//qvEBJbXNLJLm31tpez+FDKUvvZ2NeIxV42mtormtjaJbV9i/xcyj1nYS3IbqZdKruqoN3bw0Z2CUuzcS5OuyIhobmxirNBEvBLrm9KZZBNrsrsWlmJ/8K4zk7olT5UyMi3LuuP1ZOf1anRO4vq4MH8HMGHU06ak+PN55lgargGWuBe9Rnx3u626iuLqOzFTFMOuNsaEcKK1k0+osV/Kv1Ce64Y3oPD8F5wswLVlJS+lVCh31UxUy+pqf8+DeaIpL20neqnfWiD6TCZvwksr6ATYv9KUsfzdVl+4jG+wXWbR8LaF+nsMWsX0IIskSgxA8ZlhcHzcL/Q9IQw4N9n/EYFlBTKRAq6IbK2o0EXrW2O7T0tVL2vpsjKrRzlwJ3kc5h+nzpjq+7DQ876GiSYXMK0BLcorW1VpKPH34IAEzslgQPen31nwnua/SAaN0jtWGWAfOkKITk4j+Jq+95jrnShpIWbqSsHEK+nq7MK/biDlPO3SGvpV0S1bl7B0RyEgVYpxPtuP5IrnCH0Hnj+T0D0D/Wv8d0Cfig/PtE88x5AAAAABJRU5ErkJggg==)
где - унитарный оператор, действующий в гильбертовом пространстве , а - оператор, действующий из в . Даже эта задача является достаточно широкой и имеет необычные свойства. Например, если ![](data:image/png;base64,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) и ![](data:image/png;base64,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) то, как показали в работе [1], задача Коши
![](data:image/png;base64,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) (1.5)
![](data:image/png;base64,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) (1.6)
Имеет полную ортогональную систему собственных векторов, хотя, как известно классическая задача Коши
![](data:image/png;base64,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) (1.7)
![](data:image/png;base64,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) (1.8)
вольтеррова.
В настоящей работе мы рассмотрим более общую задачу Коши
![](data:image/png;base64,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) (1.9)
![](data:image/png;base64,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) , (1.10)
где - вещественная величина, 𝜆- спектральный параметр и исследуем зависимость спектральных свойств этой задачи от 𝜆, при ![](data:image/png;base64,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) результаты совпадают результатами работы [1].
Достарыңызбен бөлісу: |