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In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation \[ y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}},\quad n=0,1,..., \] where \(\left\{\alpha_n\right\}_{n\geq0}\) is a bounded sequence of positive numbers, \(k,r\) are nonnegative integers such that \(r

We consider a class of semilinear wave equations with both strongly and nonlinear weakly damped terms,associated with initial and Dirichlet boundary conditions. Under certain conditions, we show that any solution with arbitrarily high positive initial energy blows up in finite time if m < p. Furthermore, we obtain a lower bound for the blow-up time.