Existence of multiple positive solutions for Sturm–Liouville-like four-point boundary value problem with [formula omitted]-Laplacian

Abstract

In this paper, we consider the Sturm–Liouville-like four-point boundary value problem with p -Laplacian ( ϕ p ( u ′ ) ) ′ ( t ) + f ( t , u ( t ) ) = 0 , t ∈ ( 0 , 1 ) , u ( 0 ) − α u ′ ( ξ ) = 0 , u ( 1 ) + β u ′ ( η ) = 0 , where ϕ p ( s ) = | s | p − 2 s , p > 1 . By means of a fixed-point theorem for operators on a cone, the existence of multiple (at least three) positive solutions to the above boundary value problem is obtained.