Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions

Ruikuan Liu and Ruyun Ma

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: We study the existence and nonexistence of positive solutions for the following fourth‐order two‐point boundary value problem subject to nonlinear boundary conditions u′′′′(t) = λf(t, u(t)), t ∈ (0,1), u(0) = 0, u′(0) = μh(u(0)), u′′(1) = 0, u′′′(1) = μg(u(1)), where λ > 0, μ ≥ 0 are parameters, and f : [0, 1] × [0, +∞ → (0, + ∞), h : [0, + ∞ → [0, + ∞, and g : [0, + ∞ → −∞, 0] are continuous. By using the fixed‐point index theory, we prove that the problem has at least one positive solution for λ, μ sufficiently small and has no positive solution for λ large enough.

Date: 2014
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https://doi.org/10.1155/2014/972135

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:972135

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