The generalized solutions of a certain nth order Cauchy–Euler equation-Reference-Cited by-同舟云学术

The generalized solutions of a certain nth order Cauchy–Euler equation

Published:2018-10-29 Issue:02 Volume:13 Page:2050047
ISSN:1793-5571
Container-title:Asian-European Journal of Mathematics
language:en
Short-container-title:Asian-European J. Math.

Author:

Sangsuwan Amornrat¹,Nonlaopon Kamsing¹²^ORCID,Orankitjaroen Somsak³

Affiliation:

1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

2. Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand

3. Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Abstract

In this paper, we propose the generalized solutions of a certain [Formula: see text]th order Cauchy–Euler equation of the form [Formula: see text], where [Formula: see text] and [Formula: see text] are any integers with [Formula: see text], and [Formula: see text] using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of [Formula: see text]. At the end of the paper, we give some examples showing the types of solutions.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793557120500473

Reference30 articles.

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