
Multiplicity of positive solutions for elastic beam equations under inhomogeneous boundary conditions
 SUN Xiaoyue

2023, 58(4):
6573.
doi:10.6040/j.issn.16719352.0.2022.052

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This paper studies the existence of multiple positive solutions for elastic beam equations simply supported at both ends with inhomogeneous boundary conditions{Y ^{(4)}(x)=f(x,y), x∈(0,1),y(0)=0, y(1)=b, y″(0)=0, y″(1)=0,where f∈C(［0,1］×［0,∞),［0,∞)), b>0, and f(x,s) is a monotone increasing function with respect to s for a fixed x∈［0,1］. Under appropriate conditions, there exists b^{*}>0 such that the problem has at least two positive solutions for 0<b<b^{*}, at least one positive solution for b=b^{*}, and no positive solution for b>b^{*}. The proof of the main results is based on the upper and lower solution method and topological degree theory.