Some Results of Positive Solutions for a Beam Equation with Multi-Point Boundary Conditions - Zhenghao Du; Huijuan Zhu; Fanglei Wang (Mathematics, 2025)
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.