On piecewise constant delay differential equations
For systems of differential delay equations \[ z'(t) = A(t)z(t) + B(t)z([t]) + c(t) \] existence and uniqueness of solutions is proved by means of successive approximations, a variation of parameters formula together with its relation to the corresponding formula for \(B = 0\) is established, and results on asymptotic stability of the zero solution for related semilinear problems with nonlinear terms that become small as \( t \to \infty\) are proved. In addition, the paper contains a Gronwall type estimate for solutions to related integral inequalities, sufficient criteria for the oscillatory behavior of solutions, and similar results for solutions to scalar equations with two delays of the form \(z'(t) = az(t) + bz([t]) + cz(t-\tau) + f(t)\).
scientific article; zbMATH DE number 150623