The infinite solvability of the two-point boundary value problem of a class of nonlinear differential equations with variational structure was investigated.Under the assumptions that the involved nonlinear terms are odd functions and other basic conditions

the existence of infinitely many solutions was proved by using the variational method in nonlinear functional analysis

together with the topological degree theory and critical point theory

especially the Morse theory and the concept and properties of critical groups.The model generalizes many corresponding models in recent literatures and the conclusion is more universal.