Chiang Mai Journal of Science

Print ISSN: 0125-2526 | eISSN : 2465-3845

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The Distribution Solutions of Ordinary Differential Equation with Constant Coefficients

Amnuay Kananthai and Gumpol Sritanratana
* Author for corresponding; e-mail address: -
Volume: Vol.27 No.2 (DECEMBER 2000)
Opinion
DOI:
Received: 7 June 2000, Revised: -, Accepted: 28 December 2000, Published: -

Citation: Kananthai A. and Sritanratana G., The Distribution Solutions of Ordinary Differential Equation with Constant Coefficients, Chiang Mai Journal of Science, 2000; 27(2): 119-127.

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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