A change of variables in the asymptotic theory of differential equations with unbounded delays

Asymptotically exponential solutions in nonlinear integral and differential equations

“…The study of asymptotic properties of different classes of integral and differential equations is an active research area, see, e.g., [6][7][8]12,14,15,17,[24][25][26]28] and the references therein. Most of the work in this direction has been done for linear equations, and guarantees only pure exponential growth/decay of the solutions.…”

Asymptotic stability of nonlinear systems with unbounded delays

“…Various analysis techniques such as Lyapunov direct method and characteristic equation method have been utilized to derive criteria for asymptotic stability of the systems [1,11]. Even though there are some stability criteria about systems with unbounded delays [3,4,7,8], most of stability analysis in the literature aim at systems with bounded delays (see [10,13,17] and references therein). As pointed out in [3,12], stability results established for equations with bounded delays are not obviously true in general for unbounded delays.…”

Exponential solutions of equation ẏ(t)=β(t)[y(t−δ)−y(t−τ)]

“…(1) with δ = 0 satisfying Y (+∞) = +∞, that the general structure of solutions can be clarified. Namely, in accordance with [23,Theorem 4] (see investigations [8][9][10]17,18], too) every solution y =ỹ(t) of the equatioṅ…”