Existence of three positive solutions for mm-point boundary value problems on infinite intervals

In this paper, by using the Avery–Peterson fixed point theorem on a cone, we establish the existence of three positive solutions for mm-point boundary value problems on infinite intervals {(φp(x′(t)))′+ϕ(t)f(t,x(t),x′(t))=0,01,ϕ:R+→R+,f(t,u,v):R+3→R+ is a continuous function, R+=[0,+∞),αi≥0 and 0<η1<η2<⋯<ηm−2<+∞R+=[0,+∞),αi≥0 and 0<η1<η2<⋯<ηm−2<+∞ are given.