非齐次边界条件下弹性梁方程正解的多解性  

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

作　　者：孙晓玥 SUN Xiao-yue(School of Mathematics and Statistics,Xidian University,Xi'an 710126,Shaanxi,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710126

出　　处：《山东大学学报（理学版）》2023年第4期65-73,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12061064)。

摘　　要：研究带非齐次边界条件的两端简单支撑的弹性梁方程{Y(4)(x)=f(x,y),x∈(0,1),y(0)=0,y(1)=b,y"(0)=0,y"(1)=0}多个正解的存在性,其中f∈C([0,1]×[0,∞),[0,∞)),b>0,且对给定的x∈[0,1],f(x,s)关于s单调递增。在适当的条件下,证明存在b^(*)>0,使得当0<b<b^(*)时至少存在两个正解;当b=b^(*)时至少存在一个正解;当b>b^(*)时无正解。该结果的证明基于上下解方法和拓扑度理论。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 O<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 solu-tion method and topological degree theory.

关 键 词：非齐次 简单支撑 上下解 拓扑度 

分 类 号：O175.8[理学—数学]