Existence and iteration of positive solutions to a class of Sturm–Liouville-like [formula omitted]-Laplacian boundary value problems

Abstract

This paper deals with the existence and iteration of positive solutions for the following p -Laplacian differential equation: ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , t ∈ ( 0 , 1 ) , subject to the following Sturm–Liouville-like four-point boundary condition: u ( 0 ) − α u ′ ( ξ ) = 0 , u ( 1 ) + β u ′ ( η ) = 0 where ξ , η ∈ ( 0 , 1 ) . By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.