Some topological properties of solution sets in a second order differential inclusion with m-point boundary conditions

Abstract

We consider a class of m-point (m > 3) second order boundary value problem (  ) in a separable Banach space E of the formOpen image in new windowwhere F is a closed valued mapping. Under suitable compactness conditions on F we prove that the W2,1E([0,1]) -solutions of (  ) is compact and is a retract in C1E([0,1]) . A new existence result of W2,1E([0,1]) -solutions and a related relaxation problem are also provided, here F is no longer bounded.