Chiang Mai Journal of Science

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Consider the linear differential equation of the form a_ny⁽ⁿ⁾(t)+a_n-1y^(n-1)(t)+a_n-2y^(n-2)(t)+ … + a₀y(t) = c_rd ^(r) ………………………..(* ) where a_i (i = 0, 1, 2, …, n) and c_i (r = 0, 1, 2, …, m) are constants with a_n 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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