On a first order linear singular differential equation in the space K’

  • Abdourahman Haman Adji Department of Mathematics and Computer Sciences, Faculty of Sciences, University of Ngaoundéré, Ngaoundéré 454, Cameroon
  • Shankishvili Lamara Dmitrievna Department of Mathematics, Georgian Technical University, Tbilisi 0171, Georgia
Ariticle ID: 88
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Keywords: test functions, generalized functions, Dirac-delta function, Fourier transform, zero-centered solution

Abstract

We propose in this work to describe all the generalized-function solutions of the non-homogeneous first-order linear singular differential equation with A, B two real numbers, s and p∈ N,  n ≥ 1, q∈Z+, in the space of generalized functions K. In the case of a second right-hand side consisting of an s-order derivative of the Dirac-delta function, we have completely investigated the considered equation when we look for the solution in the form of y(x)=∑k=0NCkδ(k)(x), with the unknown coefficients Ckwhich we have determined case by case, taking into account the relationship between the parameters inside. On the basis of what has been done, we focus our present research on applying the principle of superposition of the solutions that is conducting us to the awaited result when we also maintain the classical solutions of the homogeneous equation which remains the same.

 

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Published
2023-07-28
How to Cite
Adji, A. H., & Dmitrievna, S. L. (2023). On a first order linear singular differential equation in the space K’. Journal of AppliedMath, 1(2), 88. https://doi.org/10.59400/jam.v1i2.88
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Article