Positive solutions for a nonlinear third order multipoint boundary value problem

Yang, Lingzhi; Zhang, Weiguo; Liu, Xiping; Shen, Chunfang; Chen, Hua

doi:10.2140/pjm.2011.249.177

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…This type of third order three-point boundary value problems can be seen as a particular case of multipoint problems (as in [12]), nonlocal problems (see [9]), functional problems (as in [3]), or integral equations (see [4]). Therefore all the applications for the above type of problems hold for our problem.…”

Section: Introductionmentioning

confidence: 99%

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Cabada¹,

López-Somoza²,

Minhós³

2017

J. Nonlinear Sci. Appl.

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This paper provides sufficient conditions to guarantee the existence, non-existence and multiplicity of solutions for a third order eigenvalue fully differential equation, coupled with three point boundary value conditions. Although the change of sign, some bounds for the second derivative of the Green's function are obtained, which allow to define a different kind of cone that, as far as we know, has not been previously used in the literature. The main arguments are based on the fixed point index theory for bounded and unbounded sets. Some examples are presented in order to show that the different existence theorems proved are not comparable.

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Section: Introductionmentioning

confidence: 99%

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Cabada¹,

López-Somoza²,

Minhós³

2017

J. Nonlinear Sci. Appl.

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Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

Yang

Shen

Xie

2013

Abstract and Applied Analysis

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Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O'Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

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Positive Solution for Nonlinear Third-Order Multi-Point Boundary Value Problem at Resonance

Shen¹,

Zhou²,

Fan³

et al. 2020

jaac

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Positive solutions for a nonlinear third order multipoint boundary value problem

Abstract: By using the Avery-Peterson fixed point theorem, we obtain the existence of three positive solutions for a third order multipoint boundary value problem. An example illustrates the main results.

Cited by 3 publications

References 12 publications

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Existence, non-existence and multiplicity results for a third order eigenvalue three-point boundary value problem

Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

Positive Solution for Nonlinear Third-Order Multi-Point Boundary Value Problem at Resonance

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