%0 Journal Article
%T 共振条件下的二阶多点边值问题解的存在性和多解性<br>Existence and multiplicity results for a second-order multi-point boundary value problem at resonance
%A 陈彬
%A Abuelgasimalshaby Elzebir&lt
%A br&gt
%A CHEN Bin
%A Abuelgasimalshaby Elzebir
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.308
%X 摘要： 在共振条件∑mk=1ak=1下, 运用紧向量场方程的解集连通理论对二阶多点边值问题u″(t)=f(t,u(t))+e(t), t∈［0,1］,u'(0)=0, u(1)=∑mk=1aku(ηk)建立了解的存在性和多解性结果。其中, f:［0,1］×R→R连续, e∈C(［0,1］,R), 0 1 2<… m<1, a k>0(k=1,2,…,m)。<br>Abstract: It is investigated that the existence and multiplicity results for a second-order multi-point boundary value problem at resonanceu″(t)=f(t,u(t))+e(t), t∈［0,1］,u'(0)=0, u(1)=∑mk=1aku(ηk)by the connectivity properties of solution set of parameterized families of compact vector fields. where f:［0,1］×R→R is continuous, e∈C(［0,1］,R), 0 1 2<… m<1, a k>0(k=1,2,…,m)
%K 解的存在性
%K 解集连通理论
%K 共振
%K 多解性
%K 多点边值问题
%K &lt
%K br&gt
%K existence of solutions
%K multiplicity results
%K at resonance
%K connectivity properties of solution set
%K multi-point boundary value problem
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.308