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In this paper, we investigate general decay rates of solutions for a quasilinear viscoelastic equation with nonlinear weak damping.

SUMMARYWe consider a von Karman plate equation with a boundary memory condition. We prove the existence of solutions using the Galerkin method and then investigate the asymptotic behaviour of the corresponding solutions by choosing suitable Lyapunov functional.

In this paper, we prove the existence of anti-periodic solutions to a hyperbolic quasi-linear hemivariational inequalities by using the Faedo-Galerkin method. Then, we investigate optimal control problems governed by the inequalities.