Periodic boundary value problems for third order ordinary differential equations with delay (Q1891439)

The paper deals whith the existence of \(2 \pi\)-periodic Carathéodory solutions for the equation \(\dddot x(t) + f(\dot x(t)) \ddot x(t) + g(t, \dot x(t - \tau)) + h(x(t)) = p(t)\) under some conditions on the asymptotic behaviour of \(x^{-1} g(t,x)\) for \(| x | \to \infty\). The proof is achieved by the Leray-Schauder principle in the frame of the coincidence degree theory. The uniqueness is also examined.