MULTIPLICITY RESULTS FOR FOURTH ORDER PROBLEMS RELATED TO THE THEORY OF DEFORMATIONS BEAMS

被引：7

作者：

Cabada, Alberto ^{[1
]}

Jebari, Rochdi ^{[2
]}

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Inst Matemat, Dept Estat Analise Matemat & Optimizac, Santiago De Compostela 15782, Spain

[2] Univ Tunis El Manar, Fac Sci Tunis, Campus Univ 2092, El Manar, Tunisia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 02期

关键词：

Green functions; fourth-order boundary value problem; multiplicity of positive solutions; fixed-point index theory; Leggett-Williams fixed point theorem; cone; BOUNDARY-VALUE-PROBLEMS; POSITIVE SOLUTIONS;

D O I：

10.3934/dcdsb.2019250

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：489 / 505

页数：17

共 21 条

[1] EXISTENCE AND UNIQUENESS THEOREMS FOR 4TH-ORDER BOUNDARY-VALUE-PROBLEMS
AFTABIZADEH, AR
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 116 (02) : 415 - 426
[2] On positive solutions of some nonlinear fourth-order beam equations
Bai, ZB
Wang, HY
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (02) : 357 - 368
[3] A boundary value problem for fourth-order elastic beam equations
Bonanno, Gabriele
Di Bella, Beatrice
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 343 (02) : 1166 - 1176
[4] Cabada A, 2014, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-1-4614-9506-2
[5] Cabada A., 2016, BOUND VALUE PROBL, V2016
[6] Cabada A., 2017, ELECT J DIFFERENTIAL, V2017
[7] Positivity and lower and upper solutions for fourth order boundary value problems
Cabada, Alberto
Angel Cid, J.
Sanchez, Luis
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (05) : 1599 - 1612
[8] Constant sign solutions of two-point fourth order problems
Cabada, Alberto
Fernandez-Gomez, Carlos
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 263 : 122 - 133
[9] Computation of Green's functions for boundary value problems with Mathematica
Cabada, Alberto
Angel Cid, Jose
Maquez-Villamarin, Beatriz
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (04) : 1919 - 1936
[10] Coppel W. A., 1971, Disconjugacy

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