The structure of Cauchy function of a vector quasidifferential equation |
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| Author |
makhney1@yahoo.com
National University “Lvivs'ka Polytechnika”,st. S. Bandery,12, 79013, Lviv, Ukraine, Akademia Bydgoska im. Kazimierza Wielkego, Institute,of Mathematics, pl. Weyssenhoffa 11, PL-85-072, Bydgoszcz, Poland
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| Abstract |
The representation of a Cauchy matrix-function of
a vector quasidifferential equation and its mixed
quasiderivatives in the sense of the initial equation and the
adjoint equation is constructed using a fundamental system of
solutions and their quasiderivatives. Every element of such a
matrix-function may be represented in the form of a ratio of two
determinants, where the second one is a quasiwronskian and the first one
differs from it by only one row.
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| Keywords |
Cauchy matrix-function, vector quasidifferential equation, quasiderivative
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| DOI |
doi:10.30970/ms.21.2.221-224
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Reference |
1. Шин Д. Ю. Теорема существования квази-дифференциального уравнения $n$-го порядка // ДАН СССР.~-- 1938.~-- Т.18.~-- №8.~-- С.515--518.
2. Тацiй Р. М. Узагальненi квазiдиференцiальнi рiвняння // Препр. № 2-94. Львів: іППММ АН Укра∙ни, 1994. – 56 с. 3. Таций Р. М., Пахолок Б. Б. О структуре фундаментальной матрицы квазидифференциального уравнения // Докл. АН УССР. – Серия А. – 1989. – №4. – С.25–28. 4. Tatsij R., Newiadowska I., Stasiuk M. The construction of the Cauchy function for quasidifferential equations with distributions // International school-seminar “Continued Fractions, its Generalization and Application” (19–24 August 2002., Uzhgorod). – Uzhgorod: UzhNU, 2002. – P. 28–29. |
| Pages |
221-224
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| Volume |
21
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| Issue |
2
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| Year |
2004
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| Journal |
Matematychni Studii
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| Full text of paper | |
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