Asymptotic behavior of the solutions of a partial differential equation with piecewise constant argument

Abstract

where A(t) is a k × k invertible and continuous matrix function on IR + ; B(t, s), C(t, s), and D(t, s) are k×k continuous and bounded matrix functions on IR + ×IR + ; [t] and [s] are the integral parts of t and s, respectively; and 𝑓 ∶ IR k → IR k is a continuous function. More precisely, under some conditions on the matrices A(t), B(t, s), C(t, s), and D(t, s) and the function 𝑓 , we investigate the asymptotic behavior of the solutions of the above equation.