Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities

Zhiguo Wang, Daxiong Piao, Yiqian Wang

In this paper, we prove the boundedness of all the solutions for the equation $\ddot{x}+n^{2}x+g(x)+{\psi }^{\prime }(x)=p(t)$ with the Lazer-Leach condition on $g$ and $p$, where $n\in \mathbb{N^+…