变号二阶三点边值问题正解的存在性  

Positive solutions for three point boundary value problems with nonlinearities changing sign

作　　者：苗春梅 石瑞新 MIAO Chun-mei;SHI Rui-xin(School of Mathematics,Guangdong University of Education,Guangzhou 510640,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]广东第二师范学院数学学院,广东广州510640 [2]山西大学数学科学学院,山西太原030006

出　　处：《东北师大学报（自然科学版）》2023年第3期18-23,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11001032,11801039);广东省基础与应用基础研究基金资助项目(202104335420);广东省普通高校科研平台科研项目(202104444334,202103974416).

摘　　要：研究了具有变号非线性项的三点边值问题正解的存在性,非线性项f(t,0)≥0且满足基于第一特征值的次线性条件.应用r-nowhere normal-outward紧映射不动点指数定理得到正解的存在性.The existence of a positive solution to a three-point boundary value problem with nonlinearities changing sign is studied.The nonlinearities satisfies the sublinear condition based on the first eigenvalue.By applying the fixed point index theory for r-nowhere normal-outward tight maps,the existence of a positive solution is obtained.

关 键 词：非线性项变号 三点边值问题 r-nowhere normal-outward映射 不动点指数定理 

分 类 号：O175[理学—数学]