变系数二阶常微分系统Neumann边值问题正解的存在性  

Existence of Positive Solutions of Neumann Boundary Value Problems for Second Order Ordinary Differential Systems with Variable Coefficients

作　　者：孙晓玥 SUN Xiaoyue(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）》2023年第2期221-227,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Schauder不动点定理和拓扑度理论研究变系数二阶常微分系统Neumann边值问题u″(x)+a(x)u(x)=λf(x,v(x)),x∈(0,1),v″(x)+b(x)v(x)=λg(x,u(x)),x∈(0,1),u′(0)=u′(1)=0,v′(0)=v′(1)=0正解的存在性,其中:f,g:[0,1]×R→R连续,且f(x,0)<0,g(x,0)<0;a,b∈C([0,1],[0,∞)),且在[0,1]的任何子区间上不恒为0.结果表明,在适当的条件下,存在λ_(0)>0,使得当0<λ<λ_(0)时,该问题至少有一个正解.By using the Schauder fixed point theorem and topological degree theory,the author studies the existence of positive solutions of Neumann boundary value problems for second order ordinary differential systems with variable coefficients u″(x)+a(x)u(x)=λf(x,v(x)),x∈(0,1),v″(x)+b(x)v(x)=λg(x,u(x)),x∈(0,1),u′(0)=u′(1)=0,v′(0)=v′(1)=0 where f,g:[0,1]×ℝ→ℝare continuous functions,and f(x,0)<0,g(x,0)<0;a,b∈C([0,1],[0,∞).The result shows that under suitable conditions,there existsλ_(0)>0 such that the problem has at least one positive solution for 0<λ<λ_(0).

关 键 词：变系数 拓扑度理论 半正问题 

分 类 号：O175.8[理学—数学]