Volume no :70, Issue no: 1, March (2022)

ON GENERALIZED-FUNCTION SOLUTIONS OF A FIRST ORDER LINEAR SINGULAR DIFFERENTIAL EQUATION IN THE SPACE VIA FOURIER TRANSFORM

Author's: Abdourahman
Pages: [27] - [51]
Received Date: February 23, 2022
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122244

Abstract

The main purpose of this work is to obtain and describe the solutions of the non-homogeneous first order linear singular differential equation of the following type:

with two real numbers, and in the space of generalized functions
We look for the solution of this equation in the form of with the unknown coefficients to be determined.
We also obtain and analyze the classical solutions of the homogeneous equation.

Keywords

test functions, generalized functions, Dirac delta function, Fourier transform.