抽象空间中二阶非线性奇异边值问题的正解  

Positive Solutions to Boundary Value Problems for Second-order Nonlinear Singular Differential Equations in Abstract Space

作　　者：王家玉[1] 刘衍胜[2] 

机构地区：[1]潍坊学院数学与信息科学学院,山东261061 [2]山东师范大学数学系,济南250014

出　　处：《工程数学学报》2009年第1期113-117,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571111);山东省自然科学基金(Y2006A22)

摘　　要：本文在一个特殊的Banach空间中研究了一类二阶奇异边值问题正解的存在性,其中的非线性项含有一阶导数,并且在自变量的端点处和该空间的零元处具有奇异性。通过构造一个特殊的非空凸闭集,利用Kuratowskii非紧性测度理论和Monch不动点定理,获得了该类问题正解的存在性。与已有文献相比,本文没有利用近似逼近方法。因此,即使退化到纯量空间,本文所用方法也完全不同于已有文献,并且得到了更为有效的结果。最后给出了两个例子说明其应用。This paper investigates a class of singular boundary value problems for second-order differential equations in Banach space, it is remarkable that the first derivative is also in the nonlinear term. Such problems arise in the fields of gas dynamics, Newtonian fluid mechanics, nuclear physics, the theory of boundary layer, nonlinear optics and so on. By constructing a special nonempty convex closed set and using the Kuratowskii＇s noncompact measure and the Moench＇s fixed point theorem, we obtain the existence of positive solutions to such problems. Comparing with existing literature, the approximation method is not used here. Finally, two examples are provided to demonstrate the application of the main results.

关 键 词：奇异方程 不动点 正解 

分 类 号：O175.8[理学—数学] O175.15[理学—基础数学]