Paper Type |
Opinion |
Title |
The Distribution Solutions of Ordinary Differential Equation with Constant Coefficients |
Author |
Amnuay Kananthai and Gumpol Sritanratana |
Email |
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Abstract: Consider the linear differential equation of the form any(n)(t)+an-1y(n-1)(t)+an-2y(n-2)(t)+ … + a0y(t) = crd (r) ………………………..(* ) where ai (i = 0, 1, 2, …, n) and ci (r = 0, 1, 2, …, m) are constants with an ¹ 0 and is a Dirac-delta distribution with r-th-derivatives and d (0) = d and t Î (-¥ ,¥ ). In this paper, the solutions of are investigated under the conditions of m and n and it has been found that,
(1) If n £ m then there exists the solutions of (* ) that belong to the space D' of distributions and those solutions are singular and regular distributions. (2) If n-2 < m < n then there exists the solutions of (* ) that are only the regular distributions. (3) If m £ n-2 then all solutions of (* ) are classical or continuous functions for tÎ (-¥ ,¥ ). |
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Start & End Page |
119 - 127 |
Received Date |
2000-06-07 |
Revised Date |
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Accepted Date |
2000-12-28 |
Full Text |
Download |
Keyword |
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Volume |
Vol.27 No.2 (DECEMBER 2000) |
DOI |
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Citation |
Kananthai A. and Sritanratana G., The Distribution Solutions of Ordinary Differential Equation with Constant Coefficients, Chiang Mai J. Sci., 2000; 27(2): 119-127. |
SDGs |
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