SYSTEMS OF DIFFERENTIAL EQUATIONS IN THE LEBESGUE SPACES
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Анатацыя
Herein, we investigate systems of nonautonomous differential equations with generalized coefficients using the algebra of new generalized functions. We consider a system of nonautonomous differential equations with generalized coefficients as a system of equations in differentials in the algebra of new generalized functions. The solution of such a system is a new generalized 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 generalized functions. In this paper, for the first time in the literature, we describe associated solutions of the system of nonautonomous differential equations with generalized coefficients in the Lebesgue spaces Lp(T) with functions that satisfy the linear growth condition.
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Бібліяграфічныя спасылкі
1. Antosik, P. Products of measures and fubctions of finite variations, Generalized functions and operational calculus / P. Antosik, J. Legeza // Bulgarian Academy of Science. – 1979. – P. 20–26.
2. Pandit, S G. Differential systems involving impulses / S. G. Pandit, S. G. Deo // Lecture Notes in Mathematics. Springer. – Berlin, 1982.
3. Zavalishchin, S. T. Dynamic Impulse Systems. Theory and Applications, mathematics and its Applications / S. T. Zavalishchin, A. N. Sesekin // Kluwer Academic Publishers Group, Dordrecht, 1997.
4. Das, P. S. Existence and stability of measure differential equations / P. S. Das, R. R. Sharma // Czech. Math. J. – 1972. – Vol. 22, nr 1. – P. 145–158.
5. Ligeza, J. On generalized solutions of some differential nonlinear equations of order n / J. Ligeza // Ann. Polon. Math. – 1975. – Nr 31 (2). – P. 115–120.
6. Lazakovich, N V. differentials in the algebra of generalized random processes / N. V. Lazakovich // Doklady of the National Academy of Sciencies of Belarus. – 1994. – Nr 38 (5). – P. 23–27 (in Russian).
7. Yablonski, A. Differential equations with generalized coefficients / A. Yablonski // Nonlinear analysys: theory, methods and applications. – 2005. – Nr 63 (2). – P. 171–197.
8. Bedziuk, N. Yablonski, A. Differential equations with generalized coefficients / N. Bedziuk, A. Yablonski // Nonlinear differential equations and applications NoDEA. – 2010. – Nr 17. – P. 249–270.
9. Zhuk, A. I. Systems of quasidifferential equations in the direct product of algebras of mnemofunctions. Symmetric case / A. I. Zhuk, А. К. Khmyzov // Vestn. BSU. Ser. 1, Physics. Mathematics. Informatics. – 2010. – Nr 1 (2). – S. 87–93 (in Russian).
10. Zhuk, A. I. Estimation of a convergence rate to associated solutions of differential equations with generalized coefficients in the algebra of mnemofunctions / A. I. Zhuk, O. L. Yablonski // Doklady of the National Academy of Sciencies of Belarus. – 2015. – Nr 59 (2). – P. 17–22 (in Russian).
11. Zhuk, A. I. Nonautonomous systems of differential equations in the algebra of generalized functions / A. I. Zhuk, O. L. Yablonski // Proceedings of the Institute of Mathematics. – 2011. – Nr 19 (1). – P. 43–51 (in Russian).
12. Zhuk, A. I. Associated solutions of the system of nonautonomous differential equations with generalized coefficients. Mixed case / A. I. Zhuk, O. L. Yablonski, S. A. Spaskov // BSPU Bulletin. Series 3. Physics. Mathematics. Informatics. Biology. Geography. – 2019. – Nr 3 (101). – P. 16–22 (in Russian).
13. Zhuk, A. I. Systems of differential equations in the algebra of generalized functions / A. I. Zhuk, O. L. Yablonski // Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series. – 2011. – Nr 1. – P. 12–16 (in Russian).
14. Zhuk, A. I. Differential equations with generalized coefficients in Cartesian product of algebras of mnemofunctions / A. I. Zhuk, T. I. Karimova // Vestnik of Brest State Tekhnical University. Series: Physics. Mathematics. Informatics. – 2018. – Nr 5 (112). – P. 59–62 (in Russian).
15. Zhuk, A. I. On associated solution of the system of non-autonomous differential equations in the Lebesgue spaces. / A. I. Zhuk, H. N. Zashchuk // Journal of the Belarusian State University. Mathematics and Informatics. – 2022. – 1. – 6–13. – DOI: 10.33581/2520- 6508-2022-1-5-13.
16. Karimova, T. I. About associated solutions nonhomogeneous systems of equations in differentials in the algebra of generalized stochastic processes / T. I. Karimova, O. L. Yablonski // Vestn. BSU. Ser. 1, Physics. Mathematics. Informatics. – 2009. – Nr 2. – P. 81–86 (in Russian).
17. Zhuk, A. I. Nonautonomic systems of differential equations with generalized coefficients in the algebra of mnemofunctions / A. I. Zhuk, O. L. Yablonski // Doklady of the National Academy of Sciencies of Belarus. – 2013. – Nr 57 (6). – P. 20–23 (in Russian).
18. Zhuk, A. I. About associated solutions of the system of differential equations with generalized coefficients / A. I. Zhuk, H. N. Zashchuk // Vestnik of Brest State Tekhnical University. Series: Physics. Mathematics. Informatics. – 2020. – Nr 5 (123). – P. 5–8 (in Russian).