Electron. J. Diff. Equ., Vol. 2011 (2011), No. 133, pp. 1-9.

Limit cycles and bounded trajectories for a nonlinear second-order differential equation

Henry Gonzalez

Abstract:
In this article, we determine the trajectories of maximum deviation, and the closed trajectories of maximum deviation for nonlinear differential equations of the form
$$ \ddot y+2a(t,y,\dot y) \dot y+b(t,y, \dot y)y=c(t,y,\dot y) $$
where the coefficients and the right-hand side are piecewise continuous functions in $t$ and continuous in $y,\dot y$. Also we find necessary and sufficient conditions for the boundedness of all the trajectories.

Submitted April 15, 2011. Published October 13, 2011.
Math Subject Classifications: 34C05, 70K05.
Key Words: Ordinary differential equations; phase plane analysis; limit cycles; maximum deviation trajectories.

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Henry González
Faculty of Light Industry and Environmental Protection Engineering
Obuda University
1034 Budapest, Bécsi út 96/B, Hungary
email: gonzalez.henry@rkk.uni-obuda.hu

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