  In this paper, we consider the initial-boundary problem for semilinear wave
equation with a new condition $$\alpha \int_0^{u } f(s)ds \leq uf(u) + \beta
u^2 +\alpha \sigma,$$ for some positive constants $\alpha$, $\beta$, and
$\sigma$, where $\beta < \frac{\lambda_1(\alpha -2)}{2}$ with $\lambda_1$ being
a first eigenvalue of Laplacian. By introducing a family of potential wells, we
establish the invariant sets, vacuum isolation of solutions, global existence
and blow-up solutions of semilinear wave equation for initial conditions
$E(0)<d$ and $E(0)=d$.
