Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations
The existence of periodic solutions for the third-order differential equation x¨˙+ω2x˙=μF(x,x˙,x¨) is studied. We give some conditions for this equation in order to reduce it to a second-order nonlinear differential equation. We show that the existence of periodic solutions for the second-order equa...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203107089 |
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| Summary: | The existence of periodic solutions for the third-order
differential equation x¨˙+ω2x˙=μF(x,x˙,x¨) is studied. We give some conditions for
this equation in order to reduce it to a second-order nonlinear
differential equation. We show that the existence of periodic
solutions for the second-order equation implies the existence of
periodic solutions for the above equation. Then we use the Hopf
bifurcation theorem for the second-order equation and obtain many
periodic solutions for it. Also we show that the above equation
has many homoclinic solutions if F(x,x˙,x¨) has a quadratic form. Finally, we compare our result to that of Mehri and Niksirat (2001). |
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| ISSN: | 0161-1712 1687-0425 |