带导数项共振问题的可解性
Existence results of a resonance problem with derivative terms

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。
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