On energy wave equations with non-negative non-linear terms

•Results on existences of global solutions.•Special conditions where there is uniqueness of solutions.•One rate of uniform stability for the energy.

This paper deals with the existence of at least one solution and the uniform stabilization of the energy of an initial-boundary value problem for a non-linear wave equation with non-linear boundary condition of the feedback type. The non-linearities in both waves and boundary equations behave as functions of the type |u|Rϱ for ϱ>1ϱ>1.