The Existence of <i>n</i> Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem

LI Xian; DA Juxia; ZHANG Huan

doi:10.6054/j.jscnun.2024015

Journal of South China Normal University (Natural Science Edition) > 2024 > 56(1): 123-127. > DOI: 10.6054/j.jscnun.2024015

LI Xian, DA Juxia, ZHANG Huan. The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 123-127. DOI: 10.6054/j.jscnun.2024015

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The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem

1.
College of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China
2.
Department of Basic Teaching, Lanzhou Resources and Environment Voc-Tech University, Lanzhou 730070, China

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Received Date: January 09, 2023
Available Online: April 29, 2024

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Abstract

Abstract

Applying of the monotone iterative technique, the existence of positive solutions to the fourth-order boundary value problem is studied: $\begin{gathered}u^{(4)}(t)=f(u(t)) \quad(t ? [0, 1]), \\u(0)=u(1)=0, u^{\prime \prime}(0)=u^{\prime \prime}(1)=0.\end{gathered}$ The above boundary value problem has n symmetric positive solutions under certain conditions.
- fourth-order boundary value problem,
- Green's function,
- monotone iterative technique,
- symmetric positive solutions

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