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Publication
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| Title of Article |
Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-sided Distributions via Laplace Transform |
| Date of Acceptance |
17 April 2019 |
| Journal |
| Title of Journal |
Mathematics |
| Standard |
SCOPUS |
| Institute of Journal |
MDPI AG (Basel, Switzerland) |
| ISBN/ISSN |
22277390 |
| Volume |
7 |
| Issue |
4 |
| Month |
April |
| Year of Publication |
2019 |
| Page |
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| Abstract |
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 |
Cauchy-Euler equation; Dirac delta function; distributional solutions; Laplace transform; weak solutions |
| Author |
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| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
false |
| Part of thesis |
true |
| Attach file |
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| Citation |
0
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Journal Publication
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