Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale

Study of periodic and nonnegative periodic solutions of nonlinear neutral functional differential equations via fixed points

“…Obviously, Aϕ is continuous. First by (5) and (7), a change of variable in (14) shows that (Aϕ) (t + T ) = (Aϕ) (t). That is, if ϕ ∈ P T then Aϕ is periodic with period T .…”

Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

“…The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing (see [1], [3], [5]- [9], [16], [17] and papers therein). The theory of dynamic equations unifies the theories of differential equations and difference equations.…”

Existence of positive periodic solutions for delay dynamic equations

“…The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing (see [1]- [5], [9], [10], [12] and papers therein). The theory of dynamic equations unifies the theories of differential equations and difference equations.…”

“…Motivated by the papers [1]- [5], [9], [10], [12] and the references therein, we consider the following delay dynamic equation x 4 (t) + p (t) x σ (t) + q (t) x (τ (t)) = 0, t ≥ t 0 , (1.1)…”