We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ , 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-2,
author = {Yuqiang Feng and Xincheng Ding},
title = {On the solvability of a fourth-order multi-point boundary value problem},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {13-22},
zbl = {1244.34030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-2}
}
Yuqiang Feng; Xincheng Ding. On the solvability of a fourth-order multi-point boundary value problem. Annales Polonici Mathematici, Tome 105 (2012) pp. 13-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-2/