This paper deals with multiplicity results for nonlinear elastic equations of the type
where g
i[0,1] ×
R→
R satisfies Carathéodory condition e∈L
2[0,1]. The solvability of this problem has been studied by several authors, but there isn’t any multiplicity result until now to the author’s knowledge. By combining the Lyapunov-Schmidt procedure with the technique of connected set, we establish several multiplicity results under suitable condition.