Nonexistence of Nontrivial Periodic Solutions To a Class of Nonlinear Differential Equations of Eighth Order

Abstract

By constructing a Lyapunov function, a new result is given, which guarantees the non-existence of nontrivial periodic solutions to nonlinear vector differential equation of eighth order: X((8)) + AX((7)) + BX((6)) + CX((5)) + DX((4)) + E (X) triple over dot + F((X) over dot)X + G(X)(X) over dot + H(X) = 0. An example is also established for the illustrations of topic. By this way, our findings raise a new result for the nonexistence of nontrivial periodic solutions related to this nonlinear vector differential equation of eighth order.