Existence of multiple positive solutions for multipoint boundary value problems with a one-dimensional [formula omitted]-Laplacian

Abstract

In this paper we consider the multipoint boundary value problem for a one-dimensional p -Laplacian: ( ϕ p ( u ′ ) ) ′ + a ( t ) f ( t , u ) = 0 , t ∈ ( 0 , 1 ) u ( 0 ) = 0 , u ( 1 ) = ∑ i = 1 m − 2 a i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s , p > 1 , 0 < ξ 1 < ξ 2 < ⋯ < ξ m − 2 < 1 , a i ≥ 0 , for i = 1 , 2 , … , m − 3 and a m − 2 > 0 . Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.