Periodicity and stability in neutral nonlinear differential equations by Krasnoselskii’s fixed point theorem - Mansouri,Bouzid (Universidad de La Frontera. Departamento de Matemática y Estadística., 2017)
Abstract The nonlinear neutral functional differential equation with variable delay =p(t)-a(t)u(t)-a(t)q(t)g(u(t-r(t)))-b(t)f(u(t))+b(t)q(t)f(u(t-r(t))). is investigated. By using Krasnoselskii’s fixed point theorem we obtain the existence and the asymptotic stability of periodic solutions. Sufficient conditions are established for the existence and the stability of the above equation. Our results extend some results obtained in the work (19).