一类带Neumann边界条件的半正超线性梁方程非平凡解的存在性  

Nontrivial solutions for a class of semipositone superlinear beam equations with Neumann boundary condition

作　　者：马琼 王晶晶 MA Qiong;WANG Jingjing(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,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2023年第4期416-423,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11961060)。

摘　　要：在线性算子相应主特征值条件下,运用拓扑度方法和不动点理论,获得了带Neumann边界条件的半正超线性四阶方程{y^((4))(x)+(k_(1)+k_(2))y″(x)+k_(1)k_(2)y(x)=λf(x,y(x)),0≤x≤1,y'(0)=y'(1)=y'''(0)=y'''(1)=0非平凡解与正解的存在性,其中k1,k2为常数,参数λ>0,f:[0,1]×R→R连续。Under some conditions concerning the first eigenvalue corresponding to the relevant linear operator,we obtain the existence of nontrivial solutions and positive solutions for the semipositone superlinear fourth-order equation {y^((4))(x)+(k_(1)+k_(2))y″(x)+k_(1)k_(2)y(x)=λf(x,y(x)),0≤x≤1,y'(0)=y'(1)=y'''(0)=y'''(1)=0 with Neumann boundary conditions by using the topological method and the fixed point theory,where k1 and k2 are constants,paramenter λ>0,f:[0,1]×R→R is continuous.

关 键 词：拓扑度 不动点 非平凡解和正解 欧拉-伯努利梁方程 

分 类 号：O175.8[理学—数学]