Multiple positive solutions for fourth-order three-point p-Laplacian boundary-value problems
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In this paper, we study the three-point boundary-value problem for a fourth-order one-dimensional p-Laplacian differential equation (φp(u″(t)))″ + α(t)ƒ(u(t)) = 0, t ∈ (0, 1), subject to the nonlinear boundary conditions: u(0) = ξu(1), u′(1) = ηu′(0), (φp(u″(0))′ = α1(φp(u″(δ))′, u″(1) = p-1√β1u″(δ), where φp(s) = |s|p-2s, p > 1. Using the five functional fixed point theorem due to Avery, we obtain sufficient conditions for the existence of at least three positive solutions.
CitationFeng, H., Feng, M., Jiang, M., Ge, W. (2007). Multiple positive solutions for fourth-order three-point p-Laplacian boundary-value problems. Electronic Journal of Differential Equations, 2007(23), pp. 1-10.
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