Existence and Relaxation Theorem for a Second Order Differential Inclusion

Abstract

In a separable Banach space we consider a three point boundary value problem for a second order differential inclusion of the form

We investigate the existence of solutions, when the multifunction F is unbounded-valued and satisfies a pseudo-Lipschitz property. Then, a Lipschitz case is derived and the associated relaxed problem is studied.

Keywords:

• Differential inclusion
• Pseudo-Lipschitz property
• Selection

AMS Subject Classification:

• 34A60
• 34B15
• 47H10