Distribution Solutions of Euler Equations

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Alongkot Suvarnamani and Gumpon Sritanratana


         Consider  the n^{th} order  non-homogeneous  Euler  equation  of  the  formm_{0}t^{n}y^{(n)}(t)+m_{1}t^{n-1}y^{(n-1)}(t)+\cdots +m_{n-1}ty'(t)+m_{n}y(t)=f(t)    (1)

where  m_{0}, m_{1}, m_{2}, …, m_{n}  are real number m_{0}\neq 0, t\: \epsilon \: R  and f(t) is a right-sided distribution.  By using Laplace transform, we found that a complementary function of this equation in distribution sense is investigated under the conditions on the values of m_{0}, m_{1}, m_{2}, …, and m_{n}.

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Alongkot Suvarnamani and Gumpon Sritanratana, Rajamangala University of Technology Thanyaburi


Hongsit, N. (2000). On the Lattice Plane of the Fourth Order Euler Equation. Chiang Mai University.

Kananthai, A. (1999). Distribution Solutions of the Third Order Euler Equation. Southeast Asian Bulletin of Mathematics 23.