Differential-functional inequalities for bounded vector-valued functions (Q1598251)

Summary: For the space \(\mathbb{R}^n\) ordered by a cone and some functions \(f: \mathbb{R}^{n+mn}\to \mathbb{R}^n\) and \(h_1,\dots, h_m: \mathbb{R}\to\mathbb{R}\), the author considers differential-functional inequalities of the type \[ v''+ cv'+ f(v,v(h_1),\dots, v(h_m))\leq u''+ cu'+ f(u, u(h_1),\dots, u(h_m)) \] and concludes \(u\leq v\) under suitable conditions on \(u\), \(v\), \(h_k\) and \(f\). The result can be applied to obtain existence and uniqueness results for differential-functional boundary value problems of the form \[ u''+ cu'+ f(u, u(h_1),\dots, u(h_m))= q, \] with \(u\in C^2(\mathbb{R}, \mathbb{R}^n)\) bounded.