一类悬臂梁方程的可解性  

Solvability of a Class of Cantilever Beam Equations

作　　者：沈瑾睿 SHEN Jinrui(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2024年第6期1317-1324,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061064).

摘　　要：用锥上不动点定理,研究一类悬臂梁方程{w″″(t)=λf(t,w(t)),t∈(0,1),w(0)=w′(0)=w″(1)=w(1)=0,其中λ为正参数,f∈C([0,1]×[0,∞),[0,∞)).在非线性项f满足超线性或者次线性增长条件的情形下给出其正解的存在性和多解性结果.By using the fixed point theorem on the cone,the author study a class of cantilever beam equations {w″″(t)=λf(t,w(t)),t∈(0,1),w(0)=w′(0)=w″(1)=w(1)=0,whereλis a positive parameter,f∈C([0,1]×[0,∞),[0,∞)).The existence and multiplicity results of its positive solutions are given when the nonlinear term f satisfies superlinear or sublinear growth condition.

关 键 词：悬臂梁方程 存在性 多解性 正解 锥 

分 类 号：O175.8[理学—数学]