Nonlinear three-point third-order boundary value problems

Boucherif, Abdelkader; Al-Malki, Nawal

doi:10.1016/j.amc.2007.02.039

Cited by 18 publications

(7 citation statements)

References 15 publications

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“…With the development of third-order boundary value problems, Guo et al [2] considered the existence of a positive solution to the third-order three-point boundary value problem as follows To our best knowledge, few papers can be found in the literature for three positive solutions of third-order three-point boundary value problems. Motivated greatly by the above-mentioned excellent works, in this paper, we will consider the following model…”

Section: ( )mentioning

confidence: 99%

“…With the development of boundary value problems, many scholars began to pay attention to the study of higher-order boundary value problems. The third-order three-point problems have a wide range of applications in the fields of mathematics and physics [1] [2] [3] [4] [5]. Many works on the third-order boundary value problems have been established.…”

Section: Introductionmentioning

confidence: 99%

“…and Li, J.L. (2019) Existence of Multiple Positive Solutions for Third-Order Three-Point ( ) ( ) ( ) ( ) ( ) ( ) 2 , 0 1,…”

Section: Introductionmentioning

confidence: 99%

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Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

Chen¹,

Li²

2019

JAMP

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In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

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Section: ( )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

Chen¹,

Li²

2019

JAMP

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“…For other existence results for third-order three-point BVP, one may see [2][3][4][8][9][10][12][13][14][15][16]18,19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence of triple positive solutions for a third-order three-point boundary value problem

Sun

2008

Journal of Computational and Applied Mathematics

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In this paper we investigate the existence of triple positive solutions for the nonlinear third-order three-point boundary value problemwhere δ ∈ (0, 1), η ∈ [1/2, 1) are constants. f : [0, 1] × [0, ∞) × R 2 → [0, ∞), q : (0, 1) → [0, ∞) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by using a fixed-point theorem due to Avery and Peterson, we establish results on the existence of triple positive solutions to the boundary value problem.

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“…Recently, the boundary value problems of third-order differential equations have received much attention. One may see Anderson [1], Anderson and Davis [2], Bai [3], Boucherif and Al-Malki [4], Graef and Yang [5], Grossinho and Minhos [6], Sun [13], Yao [14] and Yu et al [15], and the references therein for related results. For example, in [1], Anderson obtained some existence results for positive solutions for the following BVP…”

Section: Introductionmentioning

confidence: 99%