On a Right Euler Second Order Linear Singular Differential Equation in the Space K′


Authors: Abdourahman Haman Adji, Momo Zanguim Suzie, Shankishvili Lamara Dmitrievna

Abstract: In this article, we study the solvability of a singular second-order linear differential equation in the distributional space $$K'$$. We determine all the distributional solutions centered at zero of the equation under consideration. Several of our previous studies, whose results have been widely published in mathematical journals, address with this theme in various ways depending on the types of equations considered. To achieve the set goal, the unknown function $$y(x)=\sum_{k=0}^{N} C_k\delta^{(k)}(x)$$ is a distribution, presented as a functional and taken in the form of a finite linear combination of Dirac distributions and their ordinary derivatives. The methodology consists of substituting it into the original equation, which leads to the laborious solution of a system of equations to determine the undetermined coefficients $$C_k$$ and, once found, to give the form of the general distributional solution centered at zero.

Pages: 1-7

DOI: 10.46300/91019.2026.13.1

International Journal of Pure Mathematics, E-ISSN: 2313-0571, Volume 13, 2026, Art. #1

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