一类二阶中立型逐段常变量微分方程的伪概自守解

Pseudo almost automorphic solutions of a class of second-order neutral differential equations with piecewise constant arguments

基于微分方程的伪概自守解比概自守解更具有一般性,本文对一类二阶中立型逐段常变量微分方程的伪概自守解进行研究。通过对二阶方程降阶,依据逐段常变量微分方程的解在整数点的连续性,构造一个差分方程。借助差分方程的伪概自守序列解,讨论这类微分方程的伪概自守解的存在性和唯一性。

Pseudo almost automorphic solutions of differential equations are more general than almost automorphic solutions.Pseudo almost automorphic solutions of a class of second-order neutral differential equations with piecewise constant arguments are studied.By decreasing the order of the second-order equations and according to the continuity of solutions of the equation at the integer points,a difference equation is constructed.The existence and uniqueness of pseudo almost automorphic solutions of the considered equations are discussed by using pseudo almost automorphic sequence solutions of the difference equation.