Almost automorphy for bounded solutions to second-order neutral differential equations with piecewise constant arguments

Abstract

By introducing the method of decomposition of almost automorphic sequence, we give some results on the almost automorphy of bounded solutions for the second-order neutral differential equations with piecewise constant argument $$ (x(t)+px(t-1))''=qx([t])+f(t),quad tinmathbb{R}, $$ where [.] denotes the greatest integer function, $p, q$ are nonzero constants, and f(t) is almost automorphic. Some examples illustrate our results.

Keywords

• Almost automorphic
• neutral differential equation
• bounded solution
• piecewise constant argument