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

• Main Authors: Seksan Jhanthanam, Kamsing Nonlaopon, Somsak Orankitjaroen
• Other Authors: Khon Kaen University
• Format: Article
• Published: 2020
• Subjects: Mathematics
• Online Access: https://repository.li.mahidol.ac.th/handle/123456789/51225
• Institution: Mahidol University

© 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).