On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

AbstractWe study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations: x″(t)−px′(t)−qx(t)+f(t,xt)=0,t∈[0,∞),αx(t)−βx′(t)=ξ(t),t∈[−τ,0],limt→∞x(t)=0, and x″(t)−px′(t)−qx(t)+f(t,xt,x′t)=0,t∈[0,∞),αx(t)−βx′(t)=ξ(t),t∈[−τ,0],limt→∞x(t)=0, where p,α,β⩾0, α2+β2>0, and q>0. The fixed point theorem on cone is used