一类二阶周期边值问题正解的存在性与多解性  

Existence and multiplicity of positive solutions for a class of second-order periodic boundary value problems

作　　者：康聪聪 KANG Congcong(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,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：《山东大学学报（理学版）》2023年第6期68-76,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12061064)。

摘　　要：研究二阶周期边值问题{u″(t)+pu'(t)qu(t)=λf(t,u(t)),t∈(0.2π),u(0)=u(2π),u'(0)=u'(2π)正解的存在性与多解性,其中p,q>0是常数且满足p2>4q,λ>0是参数,f:[0,2π]×[0,+∞)→[0,+∞)连续。主要结果的证明基于锥拉伸与压缩不动点定理。KANG Congcong;College of Mathematics and Statistics,Northwest Normal University;This paper considers the existence and multiplicity of positive solutions for second-order periodic boundary value problems{u″(t)+pu'(t)qu(t)=λf(t,u(t)),t∈(0.2π),u(0)=u(2π),u'(0)=u'(2π)where p,q0 are constants and satisfy p~24q,λ0 is a parameter,f:[0,2π]×[0,+∞)→[0,+∞)is continuous.The proof of the main results are based on the fixed point theorem of cone expansion-compression.

关 键 词：二阶 周期边值问题 不动点定理 多解性 

分 类 号：O175.8[理学—数学]