This paper considers the steady Swift-Hohenberg equation u""+β~2u"+u^3-u=0.Using the dynamic approach,the authors prove that it has a homoclinic solution for eachβ∈[8^(1/4)-ε_0,8^(1/4)),whereε_0 is a small positive constant.This slightly complements Santra and Wei's result[Santra,S.and Wei,J.,Homoclinic solutions for fourth order traveling wave equations,SIAM J.Math.Anal.,41,2009,2038-2056],which stated that it admits a homoclinic solution for eachβ∈(0,β_0)whereβ_0=0.9342….
