非线性Sturm-Liouville问题的一个正解存在定理  

Existence theorem of positive solution to a nonlinear Sturm-Liouville problem

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《华东师范大学学报（自然科学版）》2009年第1期32-36,60,共6页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(10571085)

摘　　要：研究了非线性Sturm-Liouville边值问题的正解存在性,其中非线性项f(t,u)可以在t=0,t=1处奇异.通过引入非线性项在有界集合上的高度函数的积分来描述非线性项的增长变化.在极限函数lim■f(t,u)/u,lim■f(t,u)/u存在的情况下利用度理论中的Krasnosel'skii不动点定理和实变函数论中的控制收敛定理证明了一个正解存在定理.The existence of positive solution was studied for the nonlinear Sturm-Liouville boundary value problem, where the nonlinear term f（t, u） may be singular at t=0, t= 1. By introducing the integrations of height functions of nonlinear term on bounded set the growths of nonlinear term were described. By applying the Krasnoselskii fixed point theorem in degree theory and the dominated convergence theorems in real variable, an existence theorem of positive solution was proved when there are limit functions lim u→＋0f（t,u）/u and lim u→＋∞f（t,u）/u.

关 键 词：非线性常微分方程 边值问题 正解 存在性 

分 类 号：O175.8[理学—数学]