| Title of Article |
Finite Series of Distributional Solutions for Certain
Linear Differential Equations |
| Date of Acceptance |
2 October 2020 |
| Journal |
| Title of Journal |
Axioms |
| Standard |
SCOPUS |
| Institute of Journal |
MDPI (Basel, Switzerland) |
| ISBN/ISSN |
|
| Volume |
9 |
| Issue |
4 |
| Month |
|
| Year of Publication |
2020 |
| Page |
116 |
| Abstract |
In this paper, we present the distributional solutions of the linear differential equations of the forms
$$t^2y''(t)+2ty'(t)-[t^2+\nu(\nu+1)]y(t)=0$$
and
$$t^2y''(t)+3ty'(t)-(t^2+\nu^2-1)y(t)=0,$$
where $\nu \in \mathbb{N}\cup\{0\}$ and $t\in \mathbb{R}$. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of $\nu$. The results of several examples are also presented. |
| Keyword |
Dirac delta function; distributional solution; Laplace transform; power series solution |
| Author |
|
| Reviewing Status |
มีผู้ประเมินอิสระ |
| Status |
ตีพิมพ์แล้ว |
| Level of Publication |
นานาชาติ |
| citation |
false |
| Part of thesis |
true |
| Attach file |
|
| Citation |
0
|
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Publication
Journal Publication
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