# American Institute of Mathematical Sciences

February  2020, 25(2): 489-505. doi: 10.3934/dcdsb.2019250

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

 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

Received  November 2018 Revised  March 2019 Published  February 2020 Early access  November 2019

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.

Citation: Alberto Cabada, Rochdi Jebari. Multiplicity results for fourth order problems related to the theory of deformations beams. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 489-505. doi: 10.3934/dcdsb.2019250
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##### References:
Graph of $\frac{z_M'''(1)-z_M'''(0)-1}{M}$ on $[-m_0^4, m_1^4)$
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