Successive iteration and positive symmetric solution for a Sturm–Liouville-like four-point boundary value problem with a p-Laplacian operator

Abstract In this paper, we consider the following Sturm–Liouville-like four-point p -Laplacian boundary value problem with the nonlinear term f depending on the first-order derivative ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) u ′ ( t ) ) = 0 0 t 1 subject to the boundary conditions u ( 0 ) − β u ′ ( ξ ) = 0 , u ( 1 ) + β u ′ ( η ) = 0 . By using a monotone iterative technique, the existence of symmetric positive solutions and corresponding iterative schemes are obtained.

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