Existence of Periodic Solutions for Totally Nonlinear Neutral Differential Equations With Variable Delay - Ardjouni, Abdelouaheb; Djoudi, Ahcéne (Sarajevo Journal of Mathematics, 2024)
We use a modification of Krasnoselskii's fixed point theorem introduced by T. A. Burton (see [ 1] Theorem 3) to show that the totally nonlinear neutral differential equation with variable delay multline* x^′ (t)=-a(t)x^3(t)+c(t)x^′ (t-g(t))Q^′ ( x( t-g(t)) ) +G( t,x^3(t),x^3(t-g(t))) , multline* has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii's theorem. The results of [ 5] are generalized. Finally, an example is given to illustrate our result. 2000 Mathematics Subject Classification. 34K20, 45J05, 45D05