Some Topological Properties of Solution Sets in a Second Order Differential Inclusion with m-point Boundary Conditions.

We consider a class of m-point ( m > 3) second order boundary value problem ( $\cal{P}_{F}$) in a separable Banach space E of the form [MediaObject not available: see fulltext.]where F is a closed valued mapping. Under suitable compactness conditions on F we prove that the $W ^{2, 1}_E([0, 1])$-solutions of ( $\cal{P}_{F}$) is compact and is a retract in $C^1_E([0, 1])$. A new existence result of $W ^{2, 1}_E([0, 1])$-solutions and a related relaxation problem are also provided, here F is no longer bounded. [ABSTRACT FROM AUTHOR]