Kragujevac J. Math. 28 - 17 Kragujevac J. Math. 28 (2005) 215-224.

CONDITIONS OF EXISTENCE QUASIPERIODIC SOLUTIONS FOR SOME NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER AND THIRD POWER

Marija Kujumdzieva-Nikoloska1 and Jordanka Mitevska2

1Faculty of Electrical Engineering, University "St. Kiril and Methodius",
Skopje, R. Macedonia
(e-mail: marekn@etf.ukim.edu.mk)
2Faculty of Natural Sciences and Mathematics, Department of Mathematics
University "St. Kiril and Methodius", Skopje, R. Macedonia
(e-mail: jordanka@iunona.pmf.ukim.edu.mk)

Abstract. Using the condition of quasiperiodicity of the solution to the nonlinear differential equation of second order (1), we reduce it to the linear differential equation of second or first order. Then we find conditions of existence quasiperiodic solutions with a constant quasiperiod and give the form of the solutions.
Used abbreviations: differential equation (DFE), quasiperiod (QP), periodic solution (PS), quasiperiodic solution (QPS), quasiperiodic coefficient (QPC)