QUALITATIVE PROPERTIES OF SOLUTIONS OF NON LINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The thesis contains analytical study for the qualitative properties of solutions of some non-linear ordinary differential equations and systems. As a continuation for the previous studies carried by previous

authors working in this area we have established and proved new sufficient conditions for. 1 st - The existence of at least one periodic solution.

- The existence of infinitely many periodic solutions, for the generalized system of Lienard given by x = h(y)-F(x) y =- g(x).

2 nd - The boundedness of solutions and their first derivatives.

-Stability of solutions.

- The existence of at least one periodic solution .

- The non existence of any periodic solutions, for the generalized equation of Lienard of the form

x+f(x)x+h(x)+g(x)= 0 . 3 rd -The existence of infinite number of periodic solutions, for the Lienard's equation of the form