Existence of Periodic Solutions and Homoclinic Orbits for Third-order Nonlinear Differential Equations
نویسنده
چکیده
The existence of periodic solutions for the third-order differential equation ̇̈ x+ ω2ẋ = μF(x,ẋ, ẍ) 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,ẋ, ẍ) has a quadratic form. Finally, we compare our result to that of Mehri and Niksirat (2001).
منابع مشابه
ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS
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