  We consider a multivalued nonlinear Duffing system driven by a nonlinear
nonhomogeneous differential operator. We prove existence theorems for both the
convex and nonconvex problems (according to whether the multivalued
perturbation is convex valued or not). Also, we show that the solutions of the
nonconvex problem are dense in those of the convex (relaxation theorem). Our
work extends the recent one by Kalita-Kowalski (JMAA,
https://doi.org/10.1016/j.jmaa. 2018.01.067).

Classical Analysis and ODEs;Analysis of PDEs