Singular differential equations and differential equations in abstract space boundary value problem is an important branch of the theory of differential equations is very active in recent years, they are in biology, biomedicine, economics and space technology has been widely applied, in recent years has been rapid development. At the same time, the existence of periodic solutions for functional differential equations has been many workers concern, in the past twenty years, many experts and scholars have made a lot of sense and creative work, get a lot of results. In recent years, existence problem of infinite delay periodic solutions of neutral functional differential equations are further investigated widely.
Since the beginning of this century, many science branches in a lot of delay problems such as circuit signal system, ecological system, fuel recycling system, genetic problems. The economic phenomenon of Social Science in a delay is described as commercial sales problems, wealth distribution, the cyclical economic crisis of capitalism . Recently, functional differential equation with infinite delay and unbounded delays also follow the rise, development is very rapid. In China, some scholars such as Zheng Zuma, Fu Xilin, Li forest already began to pay attention and study of functional differential equations and obtain some research results. Especially in 1979 in Changsha held its first meeting to functional differential equations, since 2010 at the eleventh session of functional differential equation meeting in Zhangjiajie, to a certain extent, promote the research and development of our country's functional differential equations. But there are many problems in need of many experts and scholars to further research and improvement. Study on the behavior of solutions of functional differential equations is an important aspect of qualitative theory of functional differential equations, not only has theoretical the important value but also has important practical significance. Periodic phenomena in nature and people The production practice frequently appear as the economic crisis occurred periodically, periodic changes in species number and so on. So the periodic solution of functional differential equation theory has become one important research topic in the theory of differential equation and its applications. Therefore, the existence of periodic solutions of functional differential equations, not only has the important theory significance, but also an important application value.
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