Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional -Laplacian

In this paper, we consider the multipoint boundary value problem for one-dimensional p -Laplacian ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , t ∈ ( 0 , 1 ) , subject to the boundary conditions: u ( 0 ) − ∑ i = 1 n μ i u ′ ( ξ i ) = 0 , u ( 1 ) + ∑ i = 1 n μ i u ′ ( η i ) = 0 , where ϕ p ( s ) = | s | p − 2 s , p > 1 , μ i > 0 , 0 < ξ 1 < ξ 2 < ⋯ < ξ n < 1 / 2 , ξ i + η i = 1 , i = 1 , 2 , … , n . Applying the fixed point theorem due to Avery and Peterson, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f contains the first-order derivative explicitly and the boundary condition is of Sturm–Liouville type.