Blow-up of solutions to a class of Kirchhoff equations with strong damping and nonlinear dissipation

and many authors have studied the existence and uniqueness of global solution, the blowup of the solution (see [–] and the references therein). WhenM is not a constant function, equation (.)without the damping and source terms is often called a Kirchhoff-type wave equation; it has first been introduced by Kirchhoff [] in order to describe the nonlinear vibrations of an elastic string. When ω =  or h(ut) = , the nonexistence of the global solutions of Kirchhoff equations was investigated by many authors (see [–] and the references therein). The work of Ono [, ] dealt with equation (.) with ω =  and f (u) = |u|p–u. When h(ut) = – ut or ut , Ono showed that the