JournalszaaVol. 20, No. 4pp. 1055–1063

Differential-Functional Inequalities for Bounded Vector-Valued Functions

  • Gerd Herzog

    Karlsruher Institut für Technologie (KIT), Germany
Differential-Functional Inequalities for Bounded Vector-Valued Functions cover
Download PDF

Abstract

For the space Rn\mathbb R^n ordered by a cone and some functions f:Rn+mnRnf : \mathbb R^{n+mn} \to \mathbb R^n and h1,...,hm:RRh_1, ..., h_m : \mathbb R \to \mathbb R we consider differential-functional inequalities of the type

v+cv+fv,v(1),...,v(hm)u+cu+fu,u(h1),...,u(hm)v'' + cv' + f v,v(_1), ..., v(h_m) ≤ u'' + cu' + f u, u(h_1), ..., u(h_m)

and conclude uvu ≤ v under suitable conditions on u,v,hku, v, h_k and ff. The result can be applied to obtain existence and uniqueness results for differential-functional boundary value problems of the form

u+cu+fu,u(h1),...,u(hm)=qu'' + cu' + f u, u(h_1), ..., u(h_m) = q

with uC2(R,Rnu \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