华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (3): 113-118.

• 应用数学与基础数学 • 上一篇    下一篇

一类奇异三阶常微分方程的正解存在性与多解性

姚庆六   

  1. 南京财经大学应用数学系,南京 210003
  • 收稿日期:2009-06-10 修回日期:2009-09-30 出版日期:2010-05-25 发布日期:2010-05-25
  • 通讯作者: 姚庆六

Existence and multiplicity of positive solutions to a class of singular third-order ordinary differential equations

YAO Qing-liu   

  1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, China
  • Received:2009-06-10 Revised:2009-09-30 Online:2010-05-25 Published:2010-05-25
  • Contact: YAO Qing-liu

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摘要： 考察了一类非线性三阶常微分方程的正解,其中非线性项含有一阶导数并且可以关于时间变元奇异.结论的主要条件是局部的. 换句话说,如果非线性项在某些有界集上的高度函数的积分是适当的,则这一方程至少具有1-3个正解.

关键词: 奇异常微分方程, 边值问题, 正解, 存在性, 多解性, 奇异常微分方程, 边值问题, 正解, 存在性, 多解性

Abstract: The positive solutions were considered for a class of nonlinear third-order ordinary differential equations, where the nonlinear term contains first derivative of unknown function and may be singular in the term variable. The main conditions of the results are local. In other words, the equation may have 1-3 positive solutions provided the integrations of height functions of nonlinear term on some bounded sets are appropriate.

Key words: boundary value problem, positive solution, existence, multiplicity, singular ordinary differential equation, boundary value problem, positive solution, existence, multiplicity

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