Central manifold theory for the generalized equation of Kirchhoff strings on RN

We consider the generalized quasilinear dissipative Kirchhoff's String problemutt=-∥A1/2u∥H2Au-δAut+f(u),x∈RN,t⩾0with the initial conditions u(x,0)=u0(x) and ut(x,0)=u1(x), in the case where N⩾3,δ>0. The purpose of our work is to study the stability of the initial solution u=0 for this equation using central manifold theory.