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二阶常微分方程边值问题的格林函数求法 被引量：4

Green function method for solving the boundary value problems in a kind of second order ordinary differential equation
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摘要 应用Green函数证明了一类二阶常微分方程边值问题解的存在惟一性。由Green函数把此方程的边值问题转化为等价的积分方程,继而应用压缩映射不动点定理证明了解的存在惟一性。 The existence and uniqueness of the boundary value solution for a kind of second order ordinary differential equation with Green function method are discussed here.With the Green function,we equalize the boundary value problem to the integral equation,and prove the existence and uniqueness of the solution by means of compression mapping fixed point theorem.
作者 刘丽环 常晶 高艳超
机构地区 空军航空大学基础部
出处 《长春工业大学学报》 CAS 2011年第1期102-104,共3页 Journal of Changchun University of Technology
关键词 二阶边值问题 格林函数 惟一解 boundary value problem second order Green function uniqueness existence.
分类号 O175 [理学—基础数学]
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参考文献8

  • 1程建纲.二阶微分方程边值问题的多重正解[J].应用数学学报,2003,26(2):272-279. 被引量：6
  • 2Dong H S F. Oppenheimer existence and uniqueness results for some nonlinear boundary value problems [J]. J. Math. Anal. Appl. ,1996,198:35-48.
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  • 4Li Y. On the existence and nonexistence of positive solutions for nonlinear Strum-Liouville boundary value problems [J]. J. Math. Anal. Appl. ,2005, 304:74-86.
  • 5gi Y. Positive solutions of second order boundary value problems with sign-changing nonlinear terms [J]. J. Math. Anal. Appl. ,2003,282:232-240.
  • 6Liu Yan Sheng, Yu Hui Min. Existence and u niqueness of positive solution for singular boundary value problem [J]. Computers and Mathematics with Applications,2005,50 : 133-143.
  • 7Bai Zhan Bing, Ge Wei Gao. Existence of three pos-itive solutions for some second order boundary value problems [J]. Computers and Mathematics with Applications, 2004,48 : 699-707.
  • 8Li Fu Yi, Zhang Qi, Liang Zhao Ping. Existence and multiplicity of solutions of a kind of fourth or der boundary value problem [J]. Nonlinear Analy sis,2005,62 :803-816.

二级参考文献5

  • 1Wang Junyu, Gao Wenjie. A Note on Singular Nonlinear Two-point Boundary-value Problems.Nonlinear Analysis, 2000, 39:281-287.
  • 2Liu Zhaoli, Li Fuyi. Multiple Positive Solutions of Nonlinear Two-point Boundaxy Value Problems.J. Math. Anal. Appl., 1996, 203:610--625.
  • 3Agarwal R R, O'Regan D. A Note on Existence of Nonnegative Solutions to Singular Semi-positone Problems. Nonlinear Analysis, 1999, 36(5): 615-622.
  • 4Krasnoseiskii M A, Zabreiko P P. Geometrical Methods of Nonlinear Analysis. Berlin, Heidelbreg:Springer-Verlag, 1984.
  • 5翁佩萱,蒋达清.奇异二阶泛函微分方程边值问题的多重正解[J].应用数学学报,2000,23(1):99-107. 被引量：15

共引文献5

同被引文献37

引证文献4

二级引证文献2

长春工业大学学报
2011年 第1期

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