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

Abstract

We consider the third-order differential equation $u^{{}^{\prime \prime \prime }}+a{u}^{\prime \prime }+g(u^{\prime })+cu=p(t)$, where $g:\mathbb{R}\to \mathbb{R}$ is a continuous function. We prove the existence of $\omega$-periodic solution for this equation, using coincidence degree theories.