On the second-order differential equation with piecewise constant argument and almost periodic coefficients

Green's function for second-order periodic boundary value problems with piecewise constant arguments

“…For s ∈ J , y : R → R is a solution to problem (9) if y ∈ E s and satisfies conditions in (9) taking y (s) = y (s + ) and y (t) = y (t + ), for all t ∈ Z ∪ {s}.…”

“…The following result provides an expression for the solution of (4) in terms of the solution for problem (9), with s ∈ J , under the hypotheses of Theorem 3.1.…”

“…Second-order differential equations not depending on x with piecewise constant argument given by the greatest integer function have been considered in [6][7][8][9][10]. For instance, in [10], it is studied the periodic problem…”

Boundary value problems for nonlinear second‐order functional differential equations with piecewise constant arguments

“…We cite, for instance, previous works. [9][10][11][12][13] For the mentioned works, the delay is given by the integer part function but the nonlinearity in the equation is independent of x ′ .…”

Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments

“…The study of second-order differential equations independent of the first-order derivative x with a functional dependence given by a piecewise constant argument goes back to references [11][12][13][14][15]. Here, the functional dependence considered is the greatest integer function.…”