Periodic solutions for functional-differential equations of mixed type
The paper is devoted to the study of periodic solutions for functional-differential equations of mixed type of the following form \[ x'(t)=f(t,x(t),x(t-\tau_1(t)),x(t+\tau_2(t))),\quad t\in \mathbb R, \] where \(f:\mathbb R\times\mathbb R^{3n}\to \mathbb R^n\) and \(\tau_1, \tau_2:R\to \mathbb R\) are continuous and \(\omega\)-periodic functions. Applying the coincidence degree theory of Mawhin, the authors justify the averaging principle and obtain some results on the existence of periodic solutions.
scientific article; zbMATH DE number 5141602