Existence of Positive Solutions of Boundary Value Problems for Second-order Functional Differential Equations on Infinite Intervals

In present paper, the author investigates the existence of positive solutions of boundaryvalue problems for second-order functional differential equations on infinite intervals as followsx′′ − p(t)x′ − q(t)x+ f(t, xt,xt) = 0, t ∈ I = [0,∞),αx(t)− βx′(t) = ξ(t) ≥ 0, t ∈ [−τ, 0], ξ(0) = x(∞) = 0,where α ≥ 0, β > 0, ξ(t) ∈ C[−τ, 0]. By applying fixed point index theorem on cone and operatorspectra theorem, the author obtains the results on existence of positive solutions of boundary valueproblems.