On the Instability of Nonlinear Functional Differential Equations of Fifth Order

Abstract

The author gives sufficient conditions for non-existence of periodic solutions of two higher order nonlinear delay differential systems. Our technical approach is based on the construction of two suitable Lyapunov type functionals. An example is given to illustrate the obtained results. The main results here improve recent results found on the topic in the literature from the case of without delay to the delay case.