# Differential-Functional Inequalities for Bounded Vector-Valued Functions

### Gerd Herzog

Karlsruher Institut für Technologie (KIT), Germany

## Abstract

For the space $\mathbb R^n$ ordered by a cone and some functions $f : \mathbb R^{n+mn} \to \mathbb R^n$ and $h_1, ..., h_m : \mathbb R \to \mathbb R$ we consider differential-functional inequalities of the type

$v'' + cv' + f v,v(_1), ..., v(h_m) ≤ u'' + cu' + f u, u(h_1), ..., u(h_m)$

and conclude $u ≤ v$ 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

$u'' + cu' + f u, u(h_1), ..., u(h_m) = q$

with $u \in C^2 (\mathbb R, \mathbb R^n$ bounded.

## Cite this article

Gerd Herzog, Differential-Functional Inequalities for Bounded Vector-Valued Functions. Z. Anal. Anwend. 20 (2001), no. 4, pp. 1055–1063

DOI 10.4171/ZAA/1059