Solvability of a third-order two-point boundary value problem in Banach spaces (Q862144)

The author studies the following two-point boundary value problem for a third order differential inclusion \[ -u'''(t) \in F(t,u(t),u'(t)),\quad 0\leq t \leq 1,\quad u(0)=u'(0)=u'(1)=0, \] where \(F:[0,1]\times E \times E\to 2^E\) is a multifunction and \(E\) is an ordered Banach space. The author considers the case in which the right hand side can be discontinuous and, under suitable assumptions, the existence of solutions is established via a fixed point theorem.