【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.更多还原

【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.更多还原