weighted pseudo almost periodic solutions of second order neutral differential equations with piecewise constant argument

in this work, we establish a new existence and uniqueness theorem of weighted pseudo almost periodic solution for second order neutral differential equations with piecewise constant argument of the form d²/dt² (x(t) + px(t − 1)) = qx(2[t + 1/2])+ f (t),

where [·] denotes the greatest integer function, p, q are nonzero constants with | p |̸= 1, and f (t) is discontinuous weighted pseudo almost periodic. comparing with the known results, the condition of our result is given explicitly in terms of p, q, which seems simpler and easier to check even in the special case of pseudo almost periodicity.