On the Dirichlet problem for a second-order ordinary differential equation with discontinuous right-hand side (Q2461878)

Consider the problem \[ \begin{cases} x'' \in g(t,x,y)\\ x(0) = u,\quad x(T) = v,\quad u,v\in \mathbb{R}^{n}, \end{cases} \tag{1} \] where \(x:[0,T]\to \mathbb{R}^{n}, g:(a,b)\times \mathbb{R}^{n} \times \mathbb{R}^{n} \to \mathbb{R}^{n}\) is a given multifunction, \(a<0<T<b.\) The paper is concerned with the existence of solutions of problem (1).