| 一类非线性Sturm-Liouville边值问题的可解性 |
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| 引用本文： | 姚庆六.一类非线性Sturm-Liouville边值问题的可解性[J].周口师范学院学报,2008,25(5). |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学,应用数学系,江苏,南京,210003;周口师范学院数学系,河南,周口,466001 |
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| 摘 要： | 研究了非线性Sturm-Liouville边值问题{(p(t)u'(t))' f(t,u(t),u(t))=0,0＜t＜1,au(0)-bp(0)u,(0)=A,cu(1) dp(1)u'(1)=B.的可解性,允许非线性项f(t,u,v)在t=0和t=1处奇异.利用相关线性问题的Green函数将此问题转化为一个积分方程.利用Leray-Schauder不动点定理证明了一个新的存在定理.该定理表明只要非线性项在某个有界集合上的"高度"的积分是适当的此问题就有一个解.
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| 关 键 词： | 非线性常微分方程 边值问题 积分方程 存在定理 |
Solvability of a class of nonlinear Sturm-Liouville boundary value problems |
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| YAO Qing-liu.Solvability of a class of nonlinear Sturm-Liouville boundary value problems[J].Journal of Zhoukou Normal University,2008,25(5). |
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| Authors: | YAO Qing-liu |
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| Abstract: | The solvability is studied for a nonlinear Sturm-Liouville boundary value problem {(p(t)u'(t))'+f(t,u(t),u(t))=0,0＜t＜1,au(0)-bp(0)u,(0)=A,cu(1)+dp(1)u'(1)=B.The nonlinear termf(t,u,t,)is allowed to be singular at t=0 and t=1.By using the Green function of related linear problem,the problem is transformed into an integral equation.By applying the Leray-Schauder fixed point theorem,a new existence theorem is proved.The theorem shows that the problem has a solution provided that the integration of"height"of nonlinear term on some bounded set is appropriate. |
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| Keywords: | nonlinear ordinary differential equation boundary value problem integral equation existence theorem |
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