Geodesic
On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 6-13

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Herein, we investigate systems of non-autonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of non-autonomous differential equations with generalised coefficients as a system of equations in differentials in the algebra of new generalised functions. The solution of such a system is a new generalised function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalised functions. In this paper, for the first time in the literature, we describe associated solutions of the system of non-autonomous differential equations with generalised coefficients in the Lebesgue spaces $L_{P}(T)$.
Keywords: algebra of new generalised functions; differential equations with generalised coefficients; functions of finite variation. 
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     title = {On associated solutions of the system of non-autonomous differential equations in the {Lebesgue} spaces},
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A. I. Zhuk; H. Zashchuk. On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2022), pp. 6-13. http://geodesic.mathdoc.fr/item/BGUMI_2022_1_a0/