Periodic solutions to a kind of neutral functional differential equation in the critical case
The authors study a kind of first-order neutral functional-differential equation of the form \[ (x(t)- cx(t-\tau))'= g(t,x(t-\mu(t)))+ e(t), \tag{1} \] where \(g\in C(\mathbb{R}\times \mathbb{R}; \mathbb{R})\) with \(g(t+2\pi,x)= g(t,x)\) for all \(x\in \mathbb{R}\), \(e\) and \(\mu\) are continuous periodic functions with period \(2\pi\), and \(c,\tau\in \mathbb{R}\) are two constants. The authors investigate the existence of periodic solutions to (1) in the critical case \(| c|=1\). Using Mawhin's continuation theorem and topological degree theory, the authors obtain some new results on the existence of \(2\pi\)-periodic solutions.
scientific article; zbMATH DE number 2082156