Abstract
We investigate the structure of a general solution of systems of nonlinear difference equations with continuous argument in a neighborhood of the state of equilibrium.
Similar content being viewed by others
References
G. D. Birkhoff and W. J. Trjitzinsky, “Analytic theory of singular difference equations,”Acta Math.,60, 1–89 (1932).
W. A. Harris Jr. and Y. Sibuya, “General solution of nonlinear difference equations,”Trans. Amer. Math. Soc.,115, 62–75 (1965).
By. K. Takano, “General solution of a nonlinear difference equation of Briot-Bouquet type,”Funkc. Ekvacioj.,13, No. 3, 179–198 (1971).
By. K. Takano, “Solution containing arbitrary periodic functions of systems of nonlinear difference equations,”Funck. Ekvacioj.,13, No. 2, 137–164 (1973).
G. P. Pelyukh, “Structure of continuous solutions of one class of nonlinear difference equations,”Differents. Uravn.,30, No. 6, 1083–1085 (1994).
G. P. Pelyukh, “Representation of solutions of difference equations with continuous argument,”Differents. Uravn.,32, No. 2, 304–312 (1996).
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1368–1378, October, 1999.
Rights and permissions
About this article
Cite this article
Pelyukh, G.P. Structure of a general solution of systems of nonlinear difference equations. Ukr Math J 51, 1543–1555 (1999). https://doi.org/10.1007/BF02981687
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02981687