依赖于一阶导数二阶三点边值问题正解的存在性  

Existence of positive solutions for second-order three-point boundary value problems with dependence on the first order derivative

作　　者：纪玉德[1] 郭彦平[1] 江卫华[1] 

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《河北科技大学学报》2006年第3期185-188,共4页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金资助项目(10371030);河北省自然科学基金资助项目(A2006000298);河北省博士基金资助项目(B2004204)

摘　　要：对于二阶三点边值问题x″(t)+f(t,x,x′)=0,0≤t≤1,x(0)=0,x′(1)=αx′(η),其中f:[0,1]×[0,∞)×R→[0,∞)是连续的,0<α<1,η∈(0,1),首先给出相应的Green函数,然后通过利用锥上的Krasnoselskii′s不动点定理的推广形式,赋予非线性项f一定的增长条件,保证至少1个正解的存在性。For the second-order three-point boundary value problem{x＂（t）＋f（t,x,x′）=0,0≤t≤1,x（0）=0,x′（1）=ax′（η）,f：[0,1]×[0,∞）×R→[0,∞）is continuous,0〈α〈1,η∈（0,1）,The associated Greenrs function for the above problem is given first,and then, by using the extension of Krasnoselskii＇s fixed point theorem in a cone, growth conditions are imposed on nonlinearity f which ensure the existence of at least one positive solution.

关 键 词：边值问题 锥 不动点定理 GREEN函数 

分 类 号：O175.8[理学—数学]