ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS
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on te existence of periodic solution for certain nonlinear third order differential equations
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full textON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS
Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...
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full textInstability Results for Certain Third Order Nonlinear Vector Differential Equations
Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation ... X + F (X, Ẋ)Ẍ + G(Ẋ) + H(X) = 0. An example illustrates the results obtained.
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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 bif...
full textExistence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations
The study on periodic solutions for ordinary differential equations is a very important branch in the differential equation theory. Many results about the existence of periodic solutions for second-order differential equations have been obtained by combining the classical method of lower and upper solutions and the method of alternative problems The Lyapunov-Schmidt method as discussed by many ...
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Journal title
volume 3 issue 2
pages -
publication date 1992-12-01
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