QUALITATIVE PROPERTIES OF SOLUTIONS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The general area of interest of this thesis is the qualitative study of the solutions of the nonlinear Ordinary differential equations, especially those of the Lienard's type. The problem of qualitative study gains its importance from two facts, the first one is that many applicable problems m Engineering, Physics, Biology and Economics have been described by mathematical models in the form of non linear ordinary differential equations, the second fact is that obtaining exact analytic solution for nonlinear ordinary differential equations is in some cases are complicated and in most cases are not possible. For the above reasons qualitative study is a good way to get a good information about the solutions, such as boundedness, stability, existence of periodic solutions and also Bifurcation. The thesis consists of three chapters

In chaoter (1)

We have introduced and discussed the main previous results, definitions and approaches related to the problem of qualitative properties. In chapter (2)

We focused our attention to the problem of existence of periodic solutions for the well known Lienard's equation x• + f(x)x' + g(x) = o ,

Which is equivalent to the Lienard's system x'= y- F(x), y' = -g(x) where