First order differential equations with piecewise constant arguments and nonlinear boundary value conditions (Q534731)

Consider the boundary value problem \[ x'(t)= f(t,x(t), x([t]))\quad\text{for }t\in I= [0,T],\tag{\(*\)} \] where \(T\) is a positive number \([.]\) denotes the greatest integer function. By means of the method of (weakly coupled) lower and upper solutions, the authors establish under suitable assumptions the existence of extremal solutions and extremal quasi-solutions of \((*)\).