四阶非局部边值问题的正解的存在性  

The existence of positive solutions of nonlocal boundary value problems for the fourth order

作　　者：孙涛[1] 高飞[1] 段晓东[2] 

机构地区：[1]东北大学理学院,辽宁沈阳110004 [2]大连民族学院计算机学院,辽宁大连116600

出　　处：《山东大学学报（理学版）》2010年第12期62-66,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(60573124)

摘　　要：应用锥拉伸与锥压缩不动点定理,讨论了一类非线性四阶微分方程非局部边值问题的正解的存在性,构造了一个合适的锥和凸泛函,得到了该问题正解的存在性。The nonlocal boundary value problem for a nonlinear fourth-order ordinary differential equation is considered.The existence of positive soluations is shown to the problem above by applying a generalization of the cone expansion and compression fixed point theorem.In order to study this problem,cone and convex functional are introduced.This method is different from others which discussed the existence of positive solutions about the problem.

关 键 词：非局部边值问题 正解 锥拉伸与锥压缩 凸泛函 锥 

分 类 号：O175.8[理学—数学]