非齐次的两端固定支撑梁方程多个正解的存在性  

Existence of Multiple Positive Solutions for Clamped Beam Equation with Inhomogeneous Boundary Conditions

作　　者：李阳 LI Yang(School of Mathematics and Statistics,Xidian University,Xi’an 710126,China)

机构地区：[1]西安电子科技大学数学与统计学院,西安710126

出　　处：《吉林大学学报（理学版）》2022年第5期1050-1056,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061064)。

摘　　要：用上下解方法和拓扑度理论研究带非齐次边界条件的两端固定支撑静态梁方程{u″″(t)=f(t,u),t∈(0,1),u(0)=0,u(1)=b,u′(0)=0,u′(1)=0多个正解的存在性,其中f∈C([0,1]×[0,∞),[0,∞)),b>0.结果表明:当f满足一定的条件时,该问题存在可数多个正解.By using upper and lower solution method and topological degree theory,the author studies the existence of multiple positive solutions for clamped beam equation with inhomogeneous boundary conditions {u″″(t)=f(t,u),t∈(0,1),u(0)=0,u(1)=b,u′(0)=0,u′(1)=0,where f∈C([0,1]×[0,∞),[0,∞)),b>0.The results show that when f satisfies certain conditions,there are countable multiple positive solutions for the problem.

关 键 词：非齐次 正解 上下解方法 极大值原理 

分 类 号：O175.8[理学—数学]