Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions

Zhenghao Du, Huijuan Zhu () and Fanglei Wang
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Zhenghao Du: School of Mathematics, Hohai University, Nanjing 210098, China
Huijuan Zhu: School of Mathematics, Hohai University, Nanjing 210098, China
Fanglei Wang: School of Mathematics, Hohai University, Nanjing 210098, China

Mathematics, 2025, vol. 13, issue 13, 1-17

Abstract: In this paper, we give some results on the existence and multiplicity of positive solutions for a class of fourth-order multi-point boundary value problems with a sign-changing Green’s function. Using the fixed point theorem, we establish sufficient conditions for the existence of positive solutions in different scenarios. Finally, this article provides several specific examples to illustrate the obtained conclusions. The main innovation of this paper is to address the challenges posed by Green’s functions with changing sign, which complicate the application of standard techniques.

Keywords: multi-point boundary value problem; sign-changing Green’s function; positive solutions; fixed point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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