【摘要】 在非共振条件下运用Leray-Shauder原理讨论n阶非线性常微分方程m点边值问题u(n)(t)=f(t,u(t),u′(t),…,u(n-1)(t))+e(t)a.e.t∈(0,1)u′(0)=…=u(n-1)(0)=0,u(1)=∑m-2i=1aiu(ξi)解的存在性,其中f:[0,1]×Rn→R满足Carathéodory条件,e∈L1[0,1],n≥2,m>2,ai∈R且ai全为非正实数或非负实数,ξi∈(0,1),0<ξ1<ξ2<…<ξm-2<1(i=1,2,…,m-2).更多还原

【Abstract】 In this paper,by using the the Leray-Shauder principle,we discuss the existence of solutions of m point boundary value problems for an nth-order nonlinear ordinary differential equation of the formu(n)(t)=f(t,u(t),u′(t),…,u(n-1)(t))+e(t) a.e.t∈(0,1)u′(0)=…=u(n-1)(0)=0,u(1)=∑m-2 i=1aiu(ξi)where f: ×Rn→R satisfies the Carathéodory condition,e∈L1,ai∈R,ξi∈(0,1),i=1,2,…,m-2,0<ξ1<ξ2<…<ξm-2<1,all the ai∈R have the same sign and ∑m-2 i=1ai≠1.更多还原