Asymptotic behavior of positive solutions of sublinear differential equations of Emden–Fowler type

This paper is concerned with asymptotic analysis of positive solutions of the second-order nonlinear differential equation equation(A)x′′(t)+q(t)ϕ(x(t))=0,x′′(t)+q(t)ϕ(x(t))=0, where q:[a,∞)→(0,∞)q:[a,∞)→(0,∞) is a continuous function which is regularly varying and ϕ:(0,∞)→(0,∞)ϕ:(0,∞)→(0,∞) is a continuous increasing function which is regularly varying of index γ∈(0,1)γ∈(0,1). An application of the theory of regular variation gives the possibility of determining precise information about the asymptotic behavior at infinity of intermediate solutions of Eq. (A).