非线性项零点个数与二阶周期边值问题正解个数的关系  

Relationship between Number of Zeros of Nonlinear Term and Number of Positive Solutions of Second-Order Periodic Boundary Value Problems

作　　者：王素云[1] 魏晋滢 张艳红[1] WANG Suyun;WEI Jinying;ZHANG Yanhong(School of Mathematics,Lanzhou City University,Lanzhou 730070,China)

机构地区：[1]兰州城市学院数学学院,兰州730070

出　　处：《吉林大学学报（理学版）》2019年第2期327-330,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11761044);兰州城市学院重点建设学科项目(批准号:LZCU-ZDJSXK-201706)

摘　　要：用不动点指数定理,给出非线性二阶常微分方程周期边值问题■多个正解的存在性,其中:0<q<+∞;f∈C([0;∞),[0;∞))满足存在两个正的点列ai,bi(i=1,2,…,n),a_i<b_i≤a_(i+1)<b_(i+1),使得f(ai)=0,f(bi)=0,并且f(u)>0于(ai,bi).该结果揭示了非线性项f的零点个数与周期边值问题正解个数之间的关系.By using fixed point index theorem,we gave the existence of the multiple positive solutions for periodic boundary value problems of second-order ordinary differential equations:{u″-qu+λf(u)=0,t∈(0,T),u(0)=u(T),u′(0)=u′(T),where 0<q<+∞,f∈C([0;∞),[0;∞)),f(a i)=0,f(b i)=0 and f(u)>0 in(a i,b i)with a i,b i∈(0,∞)and a i<b i≤a i+1<b i+1 for i=1,2,…,n.The results revealed the relationship between the number of zeros of the nonlinear term f and the number of positive solutions of periodic boundary value problems.

关 键 词：常微分方程 周期边值问题 正解个数 不动点指数 

分 类 号：O175.8[理学—数学]