奇异三阶m点边值问题的可解性

Solvability of singular third-order m-point boundary value problems

研究奇异三阶m点边值问题:u(t)=f(t,u(t),u′(t),u″(t))+e(t),0<t<1,u(0)=u′(0)=0,u′(1)=∑m-2i=1αiu′(ξi),C1[0,1]解的存在性。这里函数f:[0,1]×R3→R满足Carath啨odory条件,t(1-t)e(t)∈L1(0,1),αi∈R,ξi∈(0,1),(i=1,2,…,m-2)且0<ξ1<ξ2<…<ξm-2<1是给定常数。主要结果的证明基于Leray-Schauder延拓定理。

The existence of a C1 solution of the m-point boundary value problem is studied u′″（t）=f（t,u（t）,u′（t）,u″（t））＋e（t）,t∈（0,1）,u（0）=u′（0）=0,u′（1）=∑m-2i=1αiu′（ξi）.Where f：×R3→R is a function satisfying Carathéodory＇s conditions and t（1-t）e（t）∈L1（0,1）.Let αi∈R,ξi∈（0,1）,（i=1,2,…,m-2） and 0〈ξ1〈ξ2〈…〈ξm-2〈1 be given.The proof of the main result is based on the Leray-Schauder continuation theorem.