The non-existence of periodic solutions of a certain class of n-th order differential equations

The stability of the solution of an n-th order equation is studied. By using a theorem of E. A. Barbashin and N. N. Krasovskii and the construction of a V function, the solutions of the equation are found either to tend to equilibrium or to have unbounded positive semi-orbit. The result simplifies the proof of a Theorem due to Anderson [1] and establishes the theorem with less restricted conditions. Also, we apply the ressult to the work of Shimanov [8]. Copyright © 1995 Fuzhou University.