Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation

We study the Cauchy problem of generalized Boussinesq equation utt−uxx+(uxx+f(u))xx=0utt−uxx+(uxx+f(u))xx=0, where f(u)=±|u|pf(u)=±|u|p or ±|u|p−1u±|u|p−1u, p>1p>1. By introducing a family of potential wells we obtain invariant sets, vacuum isolating and threshold result of global existence and nonexistence of solution.