On the generalized solutions of a certain fourth order Euler equations


Authors

Amphon Liangprom - Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand. Kamsing Nonlaopon - Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand.


Abstract

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 find types of solutions 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 \(k\in\mathbb{N}.\)


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ISRP Style

Amphon Liangprom, Kamsing Nonlaopon, On the generalized solutions of a certain fourth order Euler equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 8, 4077--4084

AMA Style

Liangprom Amphon, Nonlaopon Kamsing, On the generalized solutions of a certain fourth order Euler equations. J. Nonlinear Sci. Appl. (2017); 10(8):4077--4084

Chicago/Turabian Style

Liangprom, Amphon, Nonlaopon, Kamsing. "On the generalized solutions of a certain fourth order Euler equations." Journal of Nonlinear Sciences and Applications, 10, no. 8 (2017): 4077--4084


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