摘要
本文讨论了二阶隐式微分方程周期边值问题-x"(t)=f(t,x(t),x'(t),z"(t)),0<t<1正解的存在性,其中f:[0,1]×R×R×R→R连续且满足增长性条件|f(t,x,y,z)|≤Ay^2+B|z|+C,这里A,C>0,B∈[0,1).证明基于零点指数理论.获得结果和使用工具与以往文献本质不同.
In this implicit differential paper, we discuss the existence of positive solutions for the second order equation periodic boundary value problems -x″（t） = f（t, x（t）, x′（t）, x″（t））, 0〈t〈 1, wheref：[0,1]×R×R×R→R iscontinuousandf：[0,1]×R×R×R→R is assumed to satisfy the growth condition： ｜f（t, x,y, z）｜ ≤ Ay2 ＋ B｜z｜ ＋ C, with A, C 〉 0, B ∈ [0, 1） and some further conditions stated. Our proofs are based on the zero point index theory. The results obtained and our methods are essentially different from some known results.
出处
《应用数学学报》
CSCD
北大核心
2014年第5期946-955,共10页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(11401166)
山东省博士后创新项目专项基金(201303074)资助项目
关键词
零点指数
锥
周期边值问题
正解
zero point index
cone
periodic boundary value problem
positive solutions
