摘要
通过讨论高阶微分方程解的存在性和延拓性,把一阶微分方程的相关结果推广到高阶微分方程上,得到了方程解的存在性和可延拓的几个充分条件,并给出了方程饱和解存在的一个充分必要条件,最后举例说明主要结果的有效性.
In this paper, we discuss the existence and continuation of solutions of higher-order differential equations and extend correlative theory of first-order equations to such equations. Some sufficient conditions of the existence and continuation of solutions are given, and a sufficient and necessary condition of the existence of saturated solutions is obtained. Finally, several examples are given to illustrate our theoretical results.
出处
《合肥学院学报（自然科学版）》
2012年第3期1-5,13,共6页
Journal of Hefei University :Natural Sciences
基金
数学天元基金项目(11126175)
安徽大学博士科研启动经费项目(023033190181)
安徽大学青年科学研究项目(023033050055)资助
关键词
高阶微分方程
解的存在性
LIPSCHITZ条件
延拓
higher-order differential equation
existence of solution
Lipschitz condition
continuation
