Periodic solutions for a third-order differential equation without asymptotic behavior on the potential

Abstract

We consider the third-order differential equation $u^{'''} +au'' + g(u')+cu=p(t)$, where $g \colon \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function. We prove the existence of $\omega$-periodic solution for this equation, using coincidence degree theories.