Publication:
Generalized solutions of the third-order Cauchy-Euler equation in the space of right-sided distributions via laplace transform

Issued Date

2019-04-01

Resource Type

Article

ISSN

22277390

DOI

10.3390/math7040376

Other identifier(s)

2-s2.0-85066453382

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Mathematics. Vol.7, No.4 (2019)

Suggested Citation

Seksan Jhanthanam, Kamsing Nonlaopon, Somsak Orankitjaroen Generalized solutions of the third-order Cauchy-Euler equation in the space of right-sided distributions via laplace transform. Mathematics. Vol.7, No.4 (2019). doi:10.3390/math7040376 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/51225

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Title

Generalized solutions of the third-order Cauchy-Euler equation in the space of right-sided distributions via laplace transform

Author(s)

Seksan Jhanthanam
 Kamsing Nonlaopon
 Somsak Orankitjaroen

Other Contributor(s)

Khon Kaen University
 Mahidol University

Abstract

© 2019 by the authors. Using the Laplace transform technique, we investigate the generalized solutions of the third-order Cauchy-Euler equation of the form t3y'''(t) + at2y''(t) + by'(t) + cy(t) = 0, where a, b, and c ∈ Z and t ∈ ℝ. We find that the types of solutions in the space of right-sided distributions, either distributional solutions or weak solutions, depend on the values of a, b, and c. At the end of the paper, we give some examples showing the types of solutions. Our work improves the result of Kananthai (Distribution solutions of the third order Euler equation. Southeast Asian Bull. Math. 1999, 23, 627-631).

Keyword(s)

Mathematics

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URI

https://repository.li.mahidol.ac.th/handle/20.500.14594/51225

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Scopus 2019