一类非线性微分方程渐近概周期解的存在性

Existence of Asymptotically Almost Periodic Solutions for a Class of Nonlinear Differential Equations

利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性.在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论.从而得到的结果在一定程度上推广和改进了相关结果.

One of the most fundamental and important problems in differential equation theory is the properties of solution for differential equations, the existence of periodic and almost periodic type solutions for differential equations has more important significance in theory and in application. In this paper the existence of asymptotically almost periodic solution for a class of nonlinear differential equation is investigated by the ergodicity of function and dissipative condition. The existence and uniqueness conclutions of asymptotically almost periodic solution for differential equation above axe obtained under some certain conditions .In some degree, the results obtained are the generations and improvements of corresponding results.