Classifications and existence of positive solutions of higher order nonlinear iterative functional differential equations

Abstract

Classification schemes for eventually positive solutions of a class of higher-order nonlinear iterative functional differential equations of the form (r(t)x (m−1)(t))′+f(t,x(t),x(Δ(t,x(t))))=0 in the case when ∫ ∞ ds/r(s)=∞ are given in terms of their magnitudes, and necessary as well as sufficient conditions for the existence of these positive solutions are also provided.