摘要本文研究了主要一阶含参数的自治微分方程的解的存在性，以构造单调序列为主要研究工具,还运用了微分方程的上下解，数列收敛等.全文分为三个部分，第一部分为引言部分，说明了本课题所研究的背景、目的﹑意义，以及主要研究的内容和一些预备知识---定理、概念；第二部分是本文的核心内容，利用上下解方法和单调迭代数列技术讨论了一阶含参数的自治微分问题解的存在性, 主要是通过构造单调序列，并且使所构造的单调序列一致收敛到非线性方程的解，验证了该解的存在性。还列举也四个微分方程在经济方面的应用的实际例子，如商品销售预测、成本分析等，在第三部分中，我将对此方程在其他方面应用中（非经济）的作用做一个拓展如军事、鉴定方面，并且同时介绍微分方程的发展方向。最后，以第四章作为总结。43250

在验证了解的存在性后，对与一阶微分方程在实际生活中的应用进行了简单的介绍。将此方程拓展至运用层面，是对此学科在过去一段时间发展的一种肯定，证明其在研究方面的价值。

毕业论文关键词:一阶含参数自治微分方程；单调序列；收敛；极小解与极大解；上下界

Abstract  Existence theorem of existence of solutions of this paper studies the main order parameter of autonomous differential equations, to construct a monotone sequence as the main research tool, using the differential equation solution, the sequence is convergent. The full text is pided into three parts. The first part is the introduction part, the subject of the research background, purpose, significance, and the main research contents and some preliminary knowledge and concept; the second part is the core content of the upper and lower solution method and the monotone iterative sequence techniques are discussed in the order parameters of autonomous differential solution, mainly by constructing monotone sequences, and the structure of monotone sequences of uniform convergence Convergence to the nonlinear equation solution and verifies the solution existence. Also listed four differential equations in the economic application of practical examples, such as commodity sales forecast, cost analysis, in the third part, I will in this equation in the role of (non economic) in other applications do a expanding, such as military, identification and, at the same time, the development direction of differential equations. Finally, in the fourth chapter, as a summary.

In the validation of the understanding of existence, it carries on the simple introduction and first order differential equations in real life applications. Will this equation is extended to use level is this discipline in over a period of time to develop a kind of affirmation to prove its value in research.

Keywords: first order parametric autonomous differential equation; monotone sequence; convergence; maximal and minimal solutions; the upper and lower bounds

目 录

摘  要 3

Abstract 4

目录 5

第一章  引言 6

1.1课题的研究背景和意义 6

1.2主要研究内容 7

1.3预备知识及研究工具 7

1.3.1逐步逼近法 7

1.3.2存在唯一性定理 8

1.3.3单调序列原理 8

        1.3.4收敛 8

1.3.5上下解 9

第二章  一阶含参数自治微分方程的解的存在性