Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay. (English) Zbl 1248.34105

Yankson, Ernest

Opusc. Math. 32, No. 3, 617-627 (2012).

Summary: We use a variant of Krasnoselskii’s fixed point theorem by T.A. Burton to show that the nonlinear neutral differential equation with functional delay \[ x'(t) = - a(t) h(x(t)) + c(t) x'(t - g(t)) + q \left( t, x(t), x(t - g(t)) \right) \] has a periodic solution.

MSC:

34K13	Periodic solutions to functional-differential equations
34K40	Neutral functional-differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

fixed point; large contraction; periodic solution; totally nonlinear neutral equation