Periodic solutions for \(n\)-th order delay differential equations with damping terms. (English) Zbl 1249.34206

Pan, Lijun

Arch. Math., Brno 47, No. 4, 263-278 (2011).

The author proves the existence of periodic solutions of the \(n\)-th order delay differential equations \[ x^{(n)}(t)=\sum _{i=1}^s b_i\,[x^{(i)}(t)]^{2k-1}+f(x(t-\tau (t)))+p(t), \] where \(k,n,s\in {\mathbb N}\), \(s\leq n-1\), \(k\geq 2\), \(b_i\in {\mathbb R}\), \(f\) is continuous, \(p\) is continuous and periodic. The method involves a continuation theorem of J. L. Mawhin.

Reviewer: Roman Šimon-Hilscher (Brno)

MSC:

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

Keywords:

delay differential equation; periodic solution; coincidence degree