摘要
考察了三阶两点边值问题u^(?)(t)+f(t,u(t))=0,0<t<1,u′(0)=u″(0)=u(1)=0的正解,其中非线性项f(t,u)可以在t=0,t=1及u=0处奇异.利用锥压缩与锥拉伸型的Guo-Krasnosel'skii不动点定理证明了正解的存在性与多解性.结论表明正解存在性依赖于非线性项的连续部分在某些有界集上的"高度".
The positive solutions are considered for the third-order two-point boundary value problem u^m(t)+f(t,u(t)) =0,0t1,u'(0)=u"(0)=u(1) = 0,where the nonlinear term may be singular at t=0,t=1 and u=0.By applying the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type,the existence and multiplicity of positive solutions are proved.The results show that the existence of positive solutions depends upon the "heights" of the continuous part of nonlinear term on some bounded sets.
出处
《南开大学学报(自然科学版)》
CAS
CSCD
北大核心
2011年第1期92-96,共5页
Acta Scientiarum Naturalium Universitatis Nankaiensis
基金
国家自然科学基金(11071109)
关键词
奇异常微分方程
边值问题
正解
存在性
多解性
singular ordinary differential equation
boundary value problem
positive solution
existence
multiplicity