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

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Feng Y., Ding X.

Annales Polonici Mathematici

2012

tom 104

nr 1

13-22

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Ding X.

1 Feng Y.

1 2012

Wyniki wyszukiwania

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