Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative

By applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions for the one-dimensional p-Laplacian differential equation, ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , t ∈ ( 0 , 1 ) , subject to the following multipoint boundary condition, u ′ ( 0 ) = ∑ i = 1 n α i u ′ ( ξ i ) , u ( 1 ) = ∑ i = 1 n β i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s with p > 1 . The interesting point is the nonlinear term f is involved with the first-order derivative explicitly.