Existence and multiplicity of positive solutions for fourth-order boundary value problems with a fully nonlinear term

YAO Yanyan; LI Jiemei

doi:10.3969/j.issn.1000-5641.201911026

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Nov. 2020

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YAO Yanyan, LI Jiemei. Existence and multiplicity of positive solutions for fourth-order boundary value problems with a fully nonlinear term[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 38-45. doi: 10.3969/j.issn.1000-5641.201911026

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YAO Yanyan, LI Jiemei. Existence and multiplicity of positive solutions for fourth-order boundary value problems with a fully nonlinear term[J]. Journal of East China Normal University (Natural Sciences), 2020, (6): 38-45. doi: 10.3969/j.issn.1000-5641.201911026

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Existence and multiplicity of positive solutions for fourth-order boundary value problems with a fully nonlinear term

doi: 10.3969/j.issn.1000-5641.201911026

YAO Yanyan,
LI Jiemei^,

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou　730070, China

Received Date: 2019-06-03
Publish Date: 2020-11-25

Abstract

Abstract

In this paper, we discuss the fourth-order two-point boundary value problem　　　　　　　　　　　　　　　　　　　　　　　　$\left\{ {\begin{array}{*{20}{l}} {{u^{(4)}}(t) = f(t,u(t),u'(t),u''(t),u'''(t)),t \in (0,1), }\\ {u(0) = u'(0) = u''(1) = u'''(1){\rm{ = 0}}. } \end{array}} \right.$Here, the nonlinear term $f$ contains $u'$, $u''$ and $u'''$; therefore, the problem is a fourth-order boundary value problem with a fully nonlinear term. By using the two fixed point theorems of Leggett-Williams type, the existence of at least two or at least three positive solutions are obtained under the term $f$ that satisfies certain conditions. Finally, two examples are given to verify the theorems.
- fully nonlinear term,
- multiple positive solutions,
- Leggett-Williams fixed point theorem

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References(12)

References

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