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