共振条件下二阶积分边值问题解的存在性(英文)  

Existence of Solutions for Second-order Boundary Value Problems at Resonance Involving Integral Conditions

作　　者：邹玉梅[1] 崔玉军[1] 

机构地区：[1]山东科技大学统计与金融系,山东青岛266590

出　　处：《数学研究》2013年第4期333-343,共11页Journal of Mathematical Study

基　　金：supported by NSFC(11371221,11071141);the Specialized Research Foundation for the Doctoral Program of Higher Education of China(20123705110001);the Program for Scientifc Research Innovation Team in Colleges and Universities of Shandong Province;Research Award Fund for Outstanding Young Scientists of Shandong Province(BS2012SF023);Foundation of SDUST

摘　　要：利用上下解方法和带参数的紧向量场解集的连通性质研究了共振条件下一类二阶微分方程积分边值问题{u′′(t)=f(t,u(t)),t∈(0,1),u(0)=∫10u(s)dα(s),u(1)=∫10u(s)dβ(s)解的存在性.This article concerns the second-order diferential equation with integral boundary conditions {u′′（t） = f（t, u（t））, t ∈（0, 1）, u（0） = ∫10 u（s）dα（s）, u（1） = ∫10 u（s）dβ（s）. Under the resonance conditions, we apply the methods of lower and upper solutions and the connectivity properties of the solution set of parameterized families of compact vector felds to establish the existence of solutions.

关 键 词：迭合度 积分边值问题 共振 

分 类 号：O175.8[理学—数学]