Abstract

We consider a class of m-point (m > 3) second order boundary value problem (PF) in a separable Banach space E of the form where F is a closed valued mapping. Under suitable compactness conditions on F we prove that the W2,1E([0,1])-solutions of (PF) 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.