%0 Journal Article
%T 带导数项共振问题的可解性<br>Existence results of a resonance problem with derivative terms
%A 叶芙梅
%J 山东大学学报（理学版）
%D 2018
%R 10.6040/j.issn.1671-9352.0.2017.266
%X 摘要： 得到带导数项共振问题:{u″(t)=f(t,u(t),u'(t)), t∈［0,1］,u(0)=εu'(0), u(1)=αu(η)。在共振条件α(η+ε)=1+ε下解的存在性, 其中常数ε∈［0,+∞), α∈(0,∞), η∈(0,1)且αη2<1, 函数f:［0,1］×R2→R连续且满足Nagumo条件。主要结果的证明基于上下解方法和紧向量场方程的解集连通理论。<br>Abstract: This paper shows the existence results of a resonance problem with derivative terms{u″(t)=f(t,u(t),u'(t)), t∈［0,1］,u(0)=εu'(0), u(1)=αu(η).under the condition of α(η+ε)=1+ε at resonance, where ε∈［0,+∞), α∈(0,∞), η∈(0,1)are given constants, and αη<21. f:［0,1］×R2→R is continuous and satisfies the Nagumo condition. The proof of the main results is based on the method of upper and lower solutions and the connectivity theory of the solution set
%K 连通集
%K Nagumo 条件
%K 共振
%K 存在性
%K 无序上下解
%K &lt
%K br&gt
%K existence
%K resonance
%K Nagumo condition
%K connectivity
%K disordered lower and upper solutions
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2017.266