Existence of positive solutions for singular fourth-order three-point boundary value problems

  title={Existence of positive solutions for singular fourth-order three-point boundary value problems},
  author={Yan Sun and Cun Guang Zhu},
In this article, we consider the boundary value problem u(4)(t) + f (t,u(t)) = 0, 0 < t < 1, subject to the boundary conditions u(0) = u′(0) = u′′(0) = 0 and u′′(1) – αu′′(η) = λ. In this setting, 0 < η < 1 and α ∈ [0, 1 η ) are constants and λ ∈ [0, +∞) is a parameter. By imposing a sufficient structure on the nonlinearity f (t,u), we deduce the existence of at least one positive solution to the problem. The novelty in our setting lies in the fact that f (t,u) may be singular at t = 0 and t… CONTINUE READING

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