具有逐段常量的三阶微分方程解的周期性和概周期性

本文考虑了以下具有逐段常量的三阶微分方程: $$ x''(t)-a^{2} x''(t)=bx\displaystyle\left(2\left\frac{t+1}{2}\right]\right).\eqno{(1)} $$ 我们通过方程(1)对应的差分方程给出了微分方程(1)解的具体形式, 并由此得到了微分方程(1)解的周期性和概周期性的一些结果.

Periodicity and almost periodicity for solutions of third-order differential equations with piecewise constant argument

In this paper, we consider the following third-order differential equation with piecewise constant argument: $$ x''(t)-a^{2} x''(t)=bx\displaystyle\left(2\left\frac{t+1}{2}\right]\right).\eqno{(1)} $$ We first give the form of the solution of (1) in term of the solution of the corresponding difference equation. Then we give some results on the periodicity and almost periodicity for the solutions of problem (1).