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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.
⎧ $u^{(4)}(t) = f(t,u(t),u''(t))$, 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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Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
13-22
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- School of Science, Wuhan University of Science and Technology, Wuhan 430065, P.R. China
autor
- School of Science, Wuhan University of Science and Technology, Wuhan 430065, P.R. China
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-2