Existence of positive solutions for higher-order functional differential equations

AbstractUnder suitable conditions on f(t,y(t+θ)), the boundary value problem of higher-order functional differential equation (FDE) of the form (BVP)(FDE)y(n)(t)+f(t,y(t+θ))=0,t∈[0,1],θ∈[−τ,a],(BC)y(i)(0)=0,0⩽i⩽n−3,αy(n−2)(t)−βy(n−1)(t)=η(t),t∈[−τ,0],γy(n−2)(t)+δy(n−1)(t)=ξ(t),t∈[1,1+a], has at least one positive solution, where θ∈[−τ,a] is a fixed constant. Moreover, we also apply this main result to establish several existence theorems which guarantee (BVP) has multiple positive solutions