| This paper is devoted to the existence of quasi-periodic solutions of completely resonant forced nonlinear beam equations under the periodic boundary conditions.By the variational Lyapunov-Schmidt reduction,the beam operator equation can be reduced into the range equation and the bifurcation equation.Due to the completely resonant,the bifurcation equation is infinite dimensional.We decompose it into two parts,and solve the infinite part and the range equation by a contract mapping method.Then the finite part can be treated by the linking theorem.The quasi-periodic solutions are with two frequencies and can be expressed in the traveling wave form. |
