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This paper is concerned with nonlinear third order O.D.E. of the from:
x'" + gl (x')x" + g2(X)X' + g3(t,x)=e(t)
where the functions gi , i = 1, 2, 3, and e(t) are continuous and periodic with respect to
t of periodic co. One of the most
important properties of the solution of the above equation is the existence of the periodic solution. In so doing we first construct the greens function and then transform the above equation into nonlinear integral equation. Using some type of fixed point theorem (Schauder), we conclude the existence of at last one solution with periodic boundary conditions.
X(i) (O)= x(i) (?) i = 0, 1, 2.
We extend this periodic boundary condition to a periodic solution using numerical method (Runge-Kutta) to approximate this periodic solution. It is
interesting to note that periodic solution of the above equation has a vast application
in engineering and physics.We only
us the mathematical model for brakes of heavy vehicle.