Generalized Solutions of the Third-Order Cauchy-Euler Equation in the Space of Right-Sided Distributions via Laplace Transform

Seksan Jhanthanam, Kamsing Nonlaopon, Somsak Orankitjaroen
2019 Mathematics  
Using the Laplace transform technique, we investigate the generalized solutions of the third-order Cauchy-Euler equation of the form t 3 y ′ ′ ′ ( t ) + a t 2 y ′ ′ ( t ) + b y ′ ( t ) + c y ( 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
more » ... ons. Our work improves the result of Kananthai (Distribution solutions of the third order Euler equation. Southeast Asian Bull. Math. 1999, 23, 627–631).
doi:10.3390/math7040376 fatcat:jphn7nof6bgutaa2texoqyi3te