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

Abstract

Positive solutions Regularly varying solutions Slowly varying solutions Asymptotic behavior of solutions a b s t r a c tThis paper is concerned with asymptotic analysis of positive solutions of the second-order nonlinear differential equationwhere q : [a, ∞) → (0, ∞) is a continuous function which is regularly varying and φ : (0, ∞) → (0, ∞) is a continuous increasing function which is regularly varying of index 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).

Asymptotic analysis of Emden-Fowler differential equations in the framework of regular variation

“…We have the following two results obtained in the papers of Kusano and Naito [14] and Kusano and Manojlović [9], respectively. A natural question arises: Is it possible to acquire useful information about the existence and asymptotic behavior of intermediate positive solutions of type (II) for the Emden-Fowler equation (A), both superlinear and sublinear?…”

Moderately growing solutions of third-order differential equations with a singular nonlinearity and regularly varying coefficients

“…The Emden-Fowler-type equation of the second and higher order with a positive exponent in context of the regular variation was studied e.g. in [13], [14], [16], [17]. We partially extend these results to the singular equation (A).…”

Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

“…(4.9) It is easy to see that l i and L i in (4.9) satisfy the cyclic systems of equations 10) because these constants are independent of X i (t) and the choice of T and T 1 . Let us now define X to be the set of continuous vector functions (…”