Weighted pseudo almost periodic solutions of second-order neutral-delay differential equations with piecewise constant argument

Abstract

By introducing the method of decomposition of weighted pseudo almost periodic sequence, we present some existence theorems of weighted pseudo almost periodic solutions for second order neutral differential equations with piecewise constant argument of the form d 2 d t 2 ( x ( t ) + p x ( t − 1 ) ) = q x ( 2 [ t + 1 2 ] ) + f ( t ) , where | p | = 1 , [ ⋅ ] denotes the greatest integer function, q is a nonzero constant and f ( t ) is weighted pseudo almost periodic. Our results are new and can be regarded as a complement of some known results even in the special cases of almost periodicity and pseudo almost periodicity.