Existence of periodic solutions for \(n\)-th order differential equations with deviating argument. (English) Zbl 1185.34092

Chen, Xing Rong; Pan, Li Jun

Int. J. Pure Appl. Math. 55, No. 3, 319-333 (2009).

Summary: By employing the coincidence degree theory of Mawhin, we study the existence of periodic solutions for \(n\)-th order differential equations with deviating argument
\[ x^{(n)}+\sum^{n-1}_{i=2} b_ix^{(i)}(t)+f(x(t))x'(t)+g(t,x(t),x(t-\tau(t))) = p(t). \]
Some new results on the existence of periodic solutions of the equations are obtained.

MSC:

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

Keywords:

\(n\)-th order differential equations; deviating argument; periodic solution; coincidence degree