A Generalization Of Afuwape-Barbashin-Ezeilo Problem For Certain Third Order Nonlinear Vibrations

Abstract

Using frequency-domain results of Afuwape [2], a theorem of Corduneanu on abstract Volterra operators [4] we have given conditions under which the third order system
μ (x) ˙x = y − x
αy˙ = g(z − y)
z˙ = f(y − x) − gy
has a periodic solution - where the nonlinearity f satisfies a sector condition, α and g are constants. Our result constitute an application of [4] (pp. 124) and a generalization of [2].