Some multiplicity results for an elastic beam equation at resonance

This paper deals with multiplicity results for nonlinear elastic equations of the type wheregi0,1] X R R satisfies Caratheodory condition L20,1]. 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.