Asymptotic behavior of semi-canonical third-order nonlinear functional differential equations

Abstract

Asymptotic properties of solutions of the third-order functional differential equation Ly(t) + f(t)y ('(t)) = 0; where Ly(t) = (p(t)(q(t)y0(t))0)0 is a semi-canonical differential operator, are studied. The main goal is to transform the semi-canonical operator into canonical form; which simplifies the investigation of the oscillatory properties of solutions. Examples are established to illustrate the significance of the results obtained.