Distribution Solutions of Euler Equations

Alongkot Suvarnamani and Gumpon Sritanratana

Authors

Alongkot Suvarnamani and Gumpon Sritanratana Rajamangala University of Technology Thanyaburi

Keywords:

Dirac-delta function, tempered distribution, Laplace transform

Abstract

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