6. Examples 6.1. Generalized Boussinesq equation. We consider the equation (GB) * . We remember that hypothesis (H0) holds with c = min{m, α1 α2 }. Also, we assumed that the source terms f and the corresponding potential operator F do not have any particular form but they satisfy (H1). The solution in the sense of Definition 2.1 holds, see [29,25,33], then nonexistence of global solutions is due to blow-up. By Theorem 3.1, if the initial **data** are such that u 0 2 * + α 2 u 0 2 2 > 0, (u 0 , u 1 ) * + α 2 (u 0 , u 1 ) 2 > 0, and the initial energy
E 0 = 1 2 u 1 2 * + α 2 u 1 2 2 + α 3 ∇u 0 2 2 + m 2 u 0 2 * + α 1 u 0 2 2 − F (u 0 ),
is such that E 0 ∈ I δ = (α δ , β δ ), given in Theorem 3.1, then the corresponding solution is not global and blows up in finite time. Moreover, by Corollary 1, for every positive initial energy E 0 , there exists initial **data** such that imply the nonexistence of global solutions in the norm of H.