| 共振条件下多点边值问题解的存在性 |
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| 引用本文： | 薛春艳,葛渭高.共振条件下多点边值问题解的存在性[J].数学学报,2005,48(2):281-290. |
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| 作者姓名： | 薛春艳 葛渭高 |
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| 作者单位： | 北京理工大学数学系,北京理工大学数学系 北京100081,沈阳师范大学数学系沈阳110034,北京100081 |
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| 基金项目： | 国家自然科学基金资助项目(10371006) |
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| 摘 要： | 本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.
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| 关 键 词： | 边值问题 Fredholm算子 共振 |
Existence of Solutions to Multi-Point Boundary Value Problems at Resonance |
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| Chun Yan XUE.Existence of Solutions to Multi-Point Boundary Value Problems at Resonance[J].Acta Mathematica Sinica,2005,48(2):281-290. |
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| Authors: | Chun Yan XUE |
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| Institution: | Chun Yan XUE Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China Department of Mathematics, Shenyang Normal University, Shenyang 110034, P. R. China Wei Gao GE Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | The paper is concerned with the existence of solutions for the following multi-point boundary value prolem x"(t) = f(t,x(t), x'(t)) + e(t), t ∈(0,1); x'(0) = x'(ξ), x(1) =sum from i=1 to m-3 βix(ηi) where βi ∈ R, rum form i=1 to m-3βi= 1, 0 <η1<η2 <... <ηm-3 < 1, 0 <ξ< 1, and rum form i=1 to m-3βiηi=1. This is the case dim Ker L = 2. When the βi's have different signs, we prove existence results for the m-point boundary value problem at resonance by the use of Mawhin's coincidence degree theory. Since all the existence results obtained in previous papers are for the case dim Ker L=1, our work is new. |
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| Keywords: | Boundary value problem Fredholm operator Resonance |
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