Limit cycles and bounded trajectories for a nonlinear second-order differential equation
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 cont...
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Texas State University
2011-10-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2011/133/abstr.html |
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doaj-41bf5af1ddcc422789b518a31d3eb4052020-11-24T23:59:41ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-10-012011133,19Limit cycles and bounded trajectories for a nonlinear second-order differential equationHenry GonzalezIn 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. http://ejde.math.txstate.edu/Volumes/2011/133/abstr.htmlOrdinary differential equationsphase plane analysislimit cyclesmaximum deviation trajectories |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Henry Gonzalez |
| spellingShingle |
Henry Gonzalez Limit cycles and bounded trajectories for a nonlinear second-order differential equation Electronic Journal of Differential Equations Ordinary differential equations phase plane analysis limit cycles maximum deviation trajectories |
| author_facet |
Henry Gonzalez |
| author_sort |
Henry Gonzalez |
| title |
Limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| title_short |
Limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| title_full |
Limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| title_fullStr |
Limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| title_full_unstemmed |
Limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| title_sort |
limit cycles and bounded trajectories for a nonlinear second-order differential equation |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2011-10-01 |
| description |
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. |
| topic |
Ordinary differential equations phase plane analysis limit cycles maximum deviation trajectories |
| url |
http://ejde.math.txstate.edu/Volumes/2011/133/abstr.html |
| work_keys_str_mv |
AT henrygonzalez limitcyclesandboundedtrajectoriesforanonlinearsecondorderdifferentialequation |
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1725446662132858880 |