Dense linear manifolds and application to linear differential operators

Oscillation criteria are obtained for a class of functional differential equations including the generalized Emden-Fowler equation $\text{x}{}^{\mathrm{(n)}}\text{+ q(t) ¦x[g(t)]¦}{}^{\mathrm{\gamma }}\text{sgn}\text{(x[g(t)]) = 0, γ > 0}$, as a special case. The purpose of this paper is to extend and improve known fundamental oscillation criteria for superlinear, sublinear, and linear differential equations with retarded arguments.