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On the solvability of a fourth-order multi-point boundary value problem

Yuqiang FengXincheng Ding — 2012

Annales Polonici Mathematici

We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ u ( 4 ) ( t ) = f ( t , u ( t ) , u ' ' ( t ) ) , t ∈ [0,1], ⎨ u(0) = u(1) = 0, ⎩ au”(ζ₁) - bu”’(ζ₁) = 0, cu”(ζ₂) + du”’(ζ₂) = 0, where 0 ≤ ζ₁ < ζ₂ ≤ 1, f ∈ C([0,1] × [0,∞) × (-∞,0],[0,∞)). By using Guo-Krasnosel’skiĭ’s fixed point theorem on cones, some criteria are established to ensure the existence, nonexistence and multiplicity of positive solutions for this problem.

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