We are interested in considering the existence and asymptotic behavior of solutions of the equation \[ (*)\quad u_{tt}(x,t)- a(\int_{\Omega}| \nabla u(y,t)|^ 2dy)\Delta u(x,t)+2\gamma u(x,t)=f(x,t), \] \(\Omega\subset {\mathbb{R}}^ n\), \(\gamma >0\), with null- Dirichlet boundary for arbitrary data of finite energy (i.e. \((u_ 0,u_ 1,f)\in H^ 1_ 0(\Omega)\cap H^ 2(\Omega)\times H^ 1(\Omega)\times L^ 2(0,\infty;\) \(H^ 1(\Omega))\equiv D)\), which are open provided that the data are not small nor analytic. Let \(U(x,t)\) be the global solution of (*) with (large) analytic data \((U_ 0,U_ 1,\bar f)\), which exists and decays as \(t\to \infty\) if \(\bar f\) tends to zero as \(t\to \infty\). Let fix \((U_ 0,U_ 1,\bar f)\) and U. We show that if \((u_ 0,u_ 1,f)\) belongs to some (small) neighborhood of \((U_ 0,U_ 1,\bar f)\) in D, then there exists a unique solution u of (*) with the data \((u_ 0,u_ 1,f)\) saisfying u-U decays. Thus we have obtained the global existence of solutions of (*) for “many” data which are not necessarily small nor analytic.