Existence and stability of a weakly damped laminated beam with a nonlinear delay

Abstract A weakly damped laminated beam system with nonlinear time delay is studied. The existence and uniqueness are proved by Faedo–Galerkin approach. We prove that the system is stable under some specific conditions on the weight of the delay and the equal wave speeds of propagation. The general energy decay rate is established by using multiplier method and some properties of convex functions. This decay result is obtained without imposing any restrictive growth assumption on the damping term at the origin. In addition, our result improves and develops some existing results in the literature.