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 equationx‴(t)+λα(t)f(t,x(t))=0,a0λ>0 is a parameter, α∈C((a,b),R+)α∈C((a,b),R+), f∈C([a,b]×(0,+∞),R+)f∈C([a,b]×(0,+∞),R+), α(t)α(t) may be singular at t=a,bt=a,b and f(t,s)f(t,s) may be singular at s=0s=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.