Using Picard's method we obtain some results concerning sufficient conditions for the existence and uniqueness of solutions of singular differential equations in a Banach space. Also, we find some sufficient conditions for the asymptotic equivalence of singular differential equations and the corresponding ordinary differential equations.
[1] Demidovich B.P. Lectures on the mathematical theory of stability - M.: Nauka, 1967. - 472 p.
[2] Daletsky Yu.L., Krein M.G. Stability of solutions of differential equations in a Banach space. - M.: Nauka, 1970. - 534 p.
[3] Krenevych A.P. Asymptotic equivalence of solutions of linear stochastic Ito systems // UMZh.-2006. - 58, № 10. - P.1368-1384.
[4] Krenevych A.P. Asymptotic equivalence of solutions of nonlinear stochastic Ito systems // Nonlinear oscillations. Institute of Mathematics of the National Academy of Sciences of Ukraine. - 2006. - 9, № 2. - P.213-220.
[5] Krenevych A. Asymptotic Equivalence Of the solutions of The Linear Stochastic Ito Equations in the Hilbert space //Theory of Stochastic Processes. - 2007. - 13(29), № 1-2. - P.103-109.
- ACS Style
- Krenevych , A.P.; Mohylova, V.V. Asymptotic investigation of singular differential equations in Hilbert space. Bukovinian Mathematical Journal. 2018, 1
- AMA Style
- Krenevych AP, Mohylova VV. Asymptotic investigation of singular differential equations in Hilbert space. Bukovinian Mathematical Journal. 2018; 1(454).
- Chicago/Turabian Style
- Andriy Pavlovych Krenevych , Viktoriya Vitaliyivna Mohylova. 2018. "Asymptotic investigation of singular differential equations in Hilbert space". Bukovinian Mathematical Journal. 1 no. 454.