Twin monotone positive solutions to a singular nonlinear third-order differential equation

This paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third-order differential equation x (t) + λα(t)f t,x(t) = 0, a 0 is a parameter, α ∈ C((a, b),R+), f ∈ C([a, b] × (0,+∞),R+), α(t) may be singular at t = a, b and f (t,s) may be singular at s = 0. Green’s function and the fixed-point theorem of cone expansion and compression type are utilized. To illustrate the results, four nontrivial examples are included. © 2006 Elsevier Inc. All rights reserved.