Abstract
In this paper, we study the existence and iteration of 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 - 2 α i u ( ξ i ) , u ( 1 ) = ∑ i = 1 n - 2 β i u ( ξ i ) . By applying a monotone iterative method, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.
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