Remarks on extremal solutions of differential equations with advanced argument (Q997524)

The author studies the existence of extremal (minimal or maximal) continuous solutions and the uniqueness of the solution for the problem with deviated argument \[ \begin{cases} x^{\prime}(t)=f(t,x(h(t)))+g(t,x(t)),\\ x(0)=x_0,\qquad t>0,\end{cases} \] where \(h\in C(\mathbb{R}_+,\mathbb{R}_+)\) and \(f,\,g:\mathbb{R}_+\times\mathbb{R}\to\mathbb{R}\) are Carathéodory functions, which satisfy some additional assumptions.