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

Yuqiang Feng, and Xincheng Ding. "On the solvability of a fourth-order multi-point boundary value problem." Annales Polonici Mathematici 104.1 (2012): 13-22. <http://eudml.org/doc/286396>.

@article{YuqiangFeng2012,
abstract = {We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ $u^\{(4)\}(t) = f(t,u(t),u^\{\prime \prime \}(t))$, 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.},
author = {Yuqiang Feng, Xincheng Ding},
journal = {Annales Polonici Mathematici},
keywords = {positive solution; existence; nonexistence; multiplicity; fixed point theorem},
language = {eng},
number = {1},
pages = {13-22},
title = {On the solvability of a fourth-order multi-point boundary value problem},
url = {http://eudml.org/doc/286396},
volume = {104},
year = {2012},
}

TY - JOUR
AU - Yuqiang Feng
AU - Xincheng Ding
TI - On the solvability of a fourth-order multi-point boundary value problem
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 1
SP - 13
EP - 22
AB - We are concerned with the solvability of the fourth-order four-point boundary value problem ⎧ $u^{(4)}(t) = f(t,u(t),u^{\prime \prime }(t))$, 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.
LA - eng
KW - positive solution; existence; nonexistence; multiplicity; fixed point theorem
UR - http://eudml.org/doc/286396
ER -