一类不定权弹性梁方程的正解  

Positive Solutions for a Class of Elastic Beam Equations with Indefinite Weights

作　　者：杨丽娟 YANG Lijuan(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）》2021年第4期737-742,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11671322,12061064).

摘　　要：用Leray-Schauder不动点定理,讨论两端简单支撑弹性梁方程u″″+βu″-αu=λa(t)f(u),0<t<1,u(0)=u″(0)=u(1)=u″(1)=0正解的存在性,其中λ是一个正参数,α,β∈R且β<2π2,α≤-β2/4,权函数a:[0,1]→ℝ连续且不定号,f:R^(+)→R连续且f(0)>0.By using Leray-Schauder fixed point theorem,the author discusses the existence of positive solutions for the elastic beam equations simply supported at both ends u″″+βu″-αu=λa(t)f(u),0<t<1,u(0)=u″(0)=u(1)=u″(1)=0,whereλis a positive parameter,α,β∈R andβ<2π2,α≤-β2/4.The weight function a:[0,1]→R is continuous and its sign is indefinite,f:R^(+)→R is continuousand f(0)>0.

关 键 词：四阶方程 不定权 正解 LERAY-SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]