The existence of ground states for fourth-order wave equations

Focusing on the fourth-order wave equation utt+Δ2u+f(u)=0utt+Δ2u+f(u)=0, we prove the existence of ground state solutions u=u(x+ct)u=u(x+ct) for an optimal range of speeds c∈Rnc∈Rn and a variety of nonlinearities ff.