Existence theorems for \(n\)th-order discontinuous ordinary differential inclusions (Q2371078)

The author studies the following problem for an \(n\)th-order differential inclusion: \[ \begin{cases} x^{(n)}(t) \in F(t,x(t)) & \text{for a.e. } t\in J,\\ x^{(i)}(0)=x_i\in \mathbb R, & i\in \{1,\dots,n-1\}, \end{cases} \] where \(J=[0,T]\) and \(F:J \times \mathbb R\to 2^{\mathbb R}\) is a multifunction. By assuming a certain type of monotonicity conditions on the multifunction \(F\), the author proves the existence of a solution to the above problem via a fixed point theorem.