一类二阶微分系统解的存在唯一性  

Existence and Uniqueness of Solutions for a Class of Second-Order Differential Systems

作　　者：康慧君 KANG Huijun(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）》2022年第1期20-26,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,研究二阶迭代微分系统{x″(t)=f(t,x(t),x^([2])(t),y(t),y^([2])(t)),a≤t≤b,y″(t)=g(t,x(t),x^([2])(t),y(t),y^([2])(t)),a≤t≤b,满足边界条件x(a)=y(a)=a,x(b)=y(b)=b或x(a)=y(a)=b,x(b)=y(b)=a时解的存在唯一性,其中x^([2])(t)=x(x(t)).By using Schauder fixed point theorem,the author study the existence and uniqueness of solutions for second-order iterative differential system {x″(t)=f(t,x(t),x^([2])(t),y(t),y^([2])(t)),a≤t≤b,y″(t)=g(t,x(t),x^([2])(t),y(t),y^([2])(t)),a≤t≤b,satisfying the boundary conditions[JP2]x(a)=y(a)=a,x(b)=y(b)=b or x(a)=y(a)=b,x(b)=y(b)=a,where x^([2])(t)=x(x(t)).

关 键 词：二阶迭代微分系统 边值问题 存在性 SCHAUDER不动点定理 

分 类 号：O175.8[理学—数学]