英语翻译二十世纪三十年代之前,对泛函微分方程的研究内容仅限于某些特殊类型方程的特殊性质.1982年和1931年,Volt

英语翻译
二十世纪三十年代之前,对泛函微分方程的研究内容仅限于某些特殊类型方程的特殊性质.1982年和1931年,Volterra讨论了更一般的泛函微分方程,并且利用泛函微分方程与一些物理系统之间的联系,定义了能量函数以及观察系统在短时间内的渐近行为,这是泛函微分方程理论发展的一个里程碑.之后,自然科学与社会科学的许多学科中提出了大量的动力系统问题,电路信号系统,生态系统,流行病学等等.随着对这些问题的深入研究,泛函微分方程理论不断完善,得到了许多关于泛函微分方程各方面的成果.在微分方程定性理论中,周期解的存在性一直是一个重要的研究课题,几十年来一直受到国内外学者的高度关注.对于微分方程周期解的研究,已获得非常多的结果.
本章研究的带积分边界条件的边值问题是多点边值问题的推广,其中的非线性项可变号,并讨论了参数$\lambda$的取值范围,通过构造一个特殊的锥,利用平移变换和锥上的不动点定理得到了该问题正解的存在性.

Before the nineteen thirties, the content of functional differential equation is only limited to the special properties of some special type equation. In 1982 and 1931, Volterra discussed the functional differential equations with more general, and utilization of functional differential equations and some physical system combined system, defines the asymptotic behavior in the short time energy function and observation system, this is a milepost functional differential equation theory development. After that, a lot of natural science and Social Science in the power system, a lot of such as physics, circuit of signal system, ecological system, genetic, epidemiological and so on. With the further research on these problems, the theory of functional differential equations with continuously perfect, get many of the functional differential equations. In the qualitative theory of differential equations, the existence of periodic solution is always an important research topic, for decades has been highly concerned by the scholars at home and abroad. For the study of periodic solutions of differential equations, has obtained many results. This chapter studies the belt integral boundary value problem is a generalization of multi-point boundary value problems, nonlinear variable number one, And discuss the value range of the parameters of the $\lambda$, by constructing a special cone, the translation and the fixed point theorem to obtain the existence of positive solutions of the problem.