Upper and lower solution method for fourth-order four-point boundary value problems

Qin Zhang; Shihua Chen; Jinhu Lü

doi:10.1016/j.cam.2005.09.007

Upper and lower solution method for fourth-order four-point boundary value problems

Qin Zhang
, Shihua Chen^*
, Jinhu Lü

^*Corresponding author for this work

Wuhan University
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

This paper is concerned with the fourth-order ordinary differential equationu⁽⁴⁾ (t) = f (t, u (t), u^″ (t)), 0 < t < 1with the four-point boundary conditionsu (0) = u (1) = 0, au^″ (ξ₁) - bu^‴ (ξ₁) = 0, cu^″ (ξ₂) + du^‴ (ξ₂) = 0,where ξ_i ∈ [0, 1](i = 1, 2) and a, b, c, d are nonnegative constants satisfying ad + bc + ac (ξ₂ - ξ₁) > 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.

Original language	English
Pages (from-to)	387-393
Number of pages	7
Journal	Journal of Computational and Applied Mathematics
Volume	196
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2005.09.007
State	Published - 15 Nov 2006
Externally published	Yes

Keywords

Four-point boundary conditions
Fourth-order ordinary differential equation
Lower and upper solution method

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10.1016/j.cam.2005.09.007

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title = "Upper and lower solution method for fourth-order four-point boundary value problems",

abstract = "This paper is concerned with the fourth-order ordinary differential equationu(4) (t) = f (t, u (t), u″ (t)), 0 < t < 1with the four-point boundary conditionsu (0) = u (1) = 0, au″ (ξ1) - bu‴ (ξ1) = 0, cu″ (ξ2) + du‴ (ξ2) = 0,where ξi ∈ [0, 1](i = 1, 2) and a, b, c, d are nonnegative constants satisfying ad + bc + ac (ξ2 - ξ1) > 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.",

keywords = "Four-point boundary conditions, Fourth-order ordinary differential equation, Lower and upper solution method",

author = "Qin Zhang and Shihua Chen and Jinhu L{\"u}",

year = "2006",

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day = "15",

doi = "10.1016/j.cam.2005.09.007",

language = "英语",

volume = "196",

pages = "387--393",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Upper and lower solution method for fourth-order four-point boundary value problems

AU - Zhang, Qin

AU - Chen, Shihua

AU - Lü, Jinhu

PY - 2006/11/15

Y1 - 2006/11/15

N2 - This paper is concerned with the fourth-order ordinary differential equationu(4) (t) = f (t, u (t), u″ (t)), 0 < t < 1with the four-point boundary conditionsu (0) = u (1) = 0, au″ (ξ1) - bu‴ (ξ1) = 0, cu″ (ξ2) + du‴ (ξ2) = 0,where ξi ∈ [0, 1](i = 1, 2) and a, b, c, d are nonnegative constants satisfying ad + bc + ac (ξ2 - ξ1) > 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.

AB - This paper is concerned with the fourth-order ordinary differential equationu(4) (t) = f (t, u (t), u″ (t)), 0 < t < 1with the four-point boundary conditionsu (0) = u (1) = 0, au″ (ξ1) - bu‴ (ξ1) = 0, cu″ (ξ2) + du‴ (ξ2) = 0,where ξi ∈ [0, 1](i = 1, 2) and a, b, c, d are nonnegative constants satisfying ad + bc + ac (ξ2 - ξ1) > 0. Some new existence results are obtained by developing the upper and lower solution method and the monotone iterative technique.

KW - Four-point boundary conditions

KW - Fourth-order ordinary differential equation

KW - Lower and upper solution method

UR - https://www.scopus.com/pages/publications/33746239224

U2 - 10.1016/j.cam.2005.09.007

DO - 10.1016/j.cam.2005.09.007

M3 - 文章

AN - SCOPUS:33746239224

SN - 0377-0427

VL - 196

SP - 387

EP - 393

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Upper and lower solution method for fourth-order four-point boundary value problems

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Keywords

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