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In this paper, we investigate the nonlinear wave equation in a bounded domain with a time-varying delay term in the weakly nonlinear internal feedback \begin{document}$\left(|u_{t}|^{\gamma-2}u_{t}\right)_{t}-Lu-\int_{0}^{t}g(t-s)L u(s)ds+ \mu_{1} \psi(u_{t}(x, t))+ \mu_{2} \psi(u_{t}(x, t-\tau(t)))=0.$ \end{document} The asymptotic behavior of solutions is studied by using an appropriate Lyapunov functional. Moreover, we extend and improve the previous results in the literature.

Energy decay of solutions for the wave equation with a time-varying delay term in the weakly nonlinear internal feedbacks