A new multiple fixed point theorem with applications

Abstract

The purpose of this work is to establish an extension of a Bai-Ge type multiple fixed point theorem for a sum of two operators. The arguments are based upon recent fixed point index theory in cones of Banach spaces for a k-set contraction perturbed by an expansive operator. As illustration, our approach is applied to prove the existence of at least three nontrivial non-negative solutions for a class eigenvalue three-point BVPs for a class of fourth order ordinary differential equations (ODEs for short).