不具备Nagumo条件的二阶微分方程两点边值问题解的存在性
Existence of Solutions of Two Points Boundary Value Problem for Second Order Differential Equations Which Doesn’t Satisfy Nagumo’s Condition
DOI: 10.12677/PM.2018.85073, PDF,    科研立项经费支持
作者: 许国安：华侨大学数学科学学院，福建 泉州
关键词: Nagumo条件；微分不等式；边值问题；存在性；唯一性；Nagumo’s Condition； Differential Inequality； Boundary Value Problem； Existence； Uniqueness
摘要: 本文研究一类不具备Nagumo条件但满足某种替代性条件的二阶微分方程两点边值问题的解的存在性，并在一定附加条件下证明解的唯一性。
Abstract: In this paper, we study the existence of solutions of two points boundary value problems for second order differential equations without Nagumo condition but satisfying some alternative conditions, and prove the uniqueness of solutions under certain additional conditions.
文章引用：许国安. 不具备Nagumo条件的二阶微分方程两点边值问题解的存在性[J]. 理论数学, 2018, 8(5): 555-559. https://doi.org/10.12677/PM.2018.85073

参考文献

[1] Nagumo, M. (1937) Uber die Differential Gleichung y'' = f(t,y,y'). Proceedings of Physical and Mathematical Society, Japan, 19, 861-866.
[2] Jackson, L.K. (1967) Subfunction and Second-Order Ordinary Differential Inequalities. Advances in Ma-thematics, 10, 307-363.
[3] Howers, F.A. (1982) Differential of Higher Order and the Asymptotic Solution of Nonlinear Boundary Value Problems. SIAM Journal on Mathematical Analysis, 13, 61-80. [Google Scholar] [CrossRef] 
[4] Jackson, L.K. (1970) Subfunction and Third-Order Ordinary Differential Inequa-lities. Journal of Differential Equations, 8, 180-194. [Google Scholar] [CrossRef] 
[5] Zhou, Z.Y. (1993) Singular Perturbation of a Class of Forth Order Qiasilinear Boundary Value Problem. Northeastern Mathematical Journal, 9, 308-314.
[6] 章国华, F.A 侯斯. 非线性奇异摄动现象: 理论和应用[M]. 福州: 福建科学技术出版社, 1989.
[7] 尤秉礼. 常微分方程补充教程[M]. 第二版. 北京: 人民教育出版社出版, 1982: 367.
[8] M.H. 普劳特, H.F. 温伯格. 微分方程的最大值原理[M]. 北京: 科学出版社, 1985.

为你推荐