On the generalized solutions of a certain fourth order Euler equations

The Journal of Nonlinear Sciences and its Applications

Amphon Liangprom¹  Kamsing Nonlaopon¹ 

[1] Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand.

关键词: Generalized solution;    distributional solution;    Euler equation;    Dirac delta function.;   

DOI  :  10.22436/jnsa.010.08.04

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

In this paper, using Laplace transform technique, we propose the generalized solutions of the fourth order Euler differential equations \[t^4y^{(4)}(t)+t^3y'''(t)+t^2y''(t)+ty'(t)+my(t)=0,\] where \(m\) is an integer and \(t\in\mathbb{R}\). We findtypes ofsolutions depend on the values of \(m\). Precisely, we have a distributional solution for \(m=-k^4-5k^3-9k^2-4k\) and a weak solution for \(m=-k^4+5k^3-9k^2+4k,\) where \(k\in\mathbb{N}.\)

【 授权许可】

Unknown