Journal of Inequalities and Applications
Volume 5 (2000), Issue 6, Pages 581-602

Positive decreasing solutions of systems of second order singular differential equations

Takaŝi Kusano and Tomoyuki Tanigawa

Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan

Received 20 June 1999; Revised 22 August 1999

Copyright © 2000 Takaŝi Kusano and Tomoyuki Tanigawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Singular differential systems of the type (p(t)|y|α1y)=φ(t)zλ,(q(t)|z|β1z)=ψ(t)yμ() are considered in an interval [a,), where α, β, λ, μ are positive constants and p, q, φ,ψ are positive continuous functions on [a,). A positive decreasing solution of () is called proper or singular according to whether it exists on [a,) or it ceases to exist at a finite point of (a,). First, conditions are given under which there does exist a singular solution of (). Then, conditions are established for the existence of proper solutions of () which are classified into moderately decreasing solutions and strongly decreasing solutions according to the rate of their decay as t.