POINCARE-BENDIXSON THEOREM FOR CERTAIN DIFFERENTIAL-EQUATIONS OF HIGHER-ORDER

By adapting its well-known proof, the Poincare-Bendixson theorem, on the existence of periodic orbits of plane autonomous systems, is extended to vector differential equations of the form f(D)x + bΦ(g(D)x) = 0. The only restrictions placed on the vector function Φ(y) are that its Jacobian matrix should be continuous and lie within a suitably chosen ellintic ball. © 1979, Royal Society of Edinburgh. All rights reserved.