Multiplicity results for fourth order problems related to the theory of deformations beams

Alberto Cabada; Rochdi Jebari

doi:10.3934/dcdsb.2019250

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2020, Volume 25, Issue 2: 489-505. Doi: 10.3934/dcdsb.2019250

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Multiplicity results for fourth order problems related to the theory of deformations beams

Alberto Cabada^1, , and
Rochdi Jebari^2,

1.
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Galicia, Spain
2.
Faculté des Sciences de Tunis, Université de Tunis El-Manar, Campus Universitaire 2092 - El Manar, Tunisie

^* Corresponding author: Alberto Cabada
^* Corresponding author: Alberto Cabada

Received: November 2018

Revised: March 2019

Early access: November 2019

Published: February 2020

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Abstract

The main purpose of this paper is to establish the existence and multiplicity of positive solutions for a fourth-order boundary value problem with integral condition. By using a new technique of construct a positive cone, we apply the Krasnoselskii compression/expansion and Leggett-Williams fixed point theorems in cones to show our multiplicity results. Finally, a particular case is studied, and the existence of multiple solutions is proved for two different particular functions.

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Mathematics Subject Classification: Primary: 34B15, 34B27; Secondary: 34B09, 34B10.

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Figure 1. Graph of $ \frac{z_M'''(1)-z_M'''(0)-1}{M} $ on $ [-m_0^4, m_1^4) $

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