Literature cited
S. B. Norkin, “On the infinite-dimensional manifold of two-sided solutions of a nonlinear system of differential equations with a delayed argument,” in: Tenth International Conference on Nonlinear Oscillations (Varna, Bulgaria, September 1984). Abstracts, Sofia (1984), p. 146.
S. B. Norkin, “Structure of solutions of a system of differential equations with retarded argument in the neighborhood of a singular point,” Prace Stud. Vysokej Skoly Doprav. Spojov Ziline Ser. Mat.-Fyz.,3, 27–46 (1981).
S. B. Norkin, “The structure of solutions of a trinomial differential equation with retarded argument in the neighborhood of a singular point,” Prace Stud. Vysokej Skoly Doprav. Spojov Ziline Ser. Mat.-Fyz.,3, 47–54 (1981).
S. B. Norkin, “On two-sided solutions of a linear system with asymptotically constant coefficients and lag,” Czechoslovak Math. J.,33, No. 108, 58–69 (1983).
S. B. Norkin, “The space of two-sided solutions with exponential growth for t→−∞ of a linear system with an asymptotically constant matrix and lag,” in: Studies in the Theory of Differential Equations [in Russian], Moscow Highway Institute (1986), pp. 27–34.
I. Ts. Gokhberg and M. G. Krein, “Systems of integral equations on the semiline with kernels depending on the difference of the arguments,” Usp. Mat. Nauk,13, No. 2 (80), 3–72 (1958).
L. E. El'sgol'ts and S. B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments, Academic Press, New York (1973).
N. Dantinne, “Application de la méthode des approximations successive a l'intégration d'une équation différentielle aux différences, I; II; III,” Bull. Soc. R. Sci. Liege,18, No. 8–10, 363–374 (1949);18, No. 11, 445–461 (1949);19, No. 2, 119–130 (1950).
Yu. A. Ryabov, “The application of the Lyapunov-Poincaré method of small parameter to the theory of systems with lag,” Inzh. Zh.,1, No. 2, 3–15 (1961).
T. Turdiev, “Analytic solutions of certain classes of linear differential equations with retarded argument,” in: Trudy Sem. Teor. Differents. Uravnenii s Otklon. Argumentom,4, 85–95 (1967).
K. Smitalova, “Existence of complete solutions of linear differential equations with delays,” Acta Math. Univ. Comenian.,40 (41), 189–193 (1982).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matemticheskii Zhurnal, Vol. 40, No. 4, pp. 459–469, July–August, 1988.
Rights and permissions
About this article
Cite this article
Norkin, S.B. A singular one-point problem for a nonlinear system with lag. Ukr Math J 40, 393–403 (1988). https://doi.org/10.1007/BF01057203
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01057203