Sufficient conditions for exponential stability and instability of solutions of nonlinear delay ordinary differential equations

Abstract

In this thesis, inequalities regarding the solutions of the nonlinear ordi- nary di erential equation with multiple delays are obtained by means of Lyapunov functionals. These inequalities are then used to obtain su cient conditions that guarantee exponential decay of solutions to zero of the multi delay nonlinear ordinary di erential equation. In addition, a criterion for the instability of the zero solution is obtained. The results generalizes some results in the literature.