Journal of Inequalities and Applications
Volume 6 (2001), Issue 1, Pages 17-27

On the inequality of weierstrass for nonlocal functionals

G. A. Kamenskii and Ju. P. Zabrodina

Department of Differential Equations, State Moscow Institute of Aviation, Volokolamskoe Shosse 4, Moscow 125871, Russia

Received 28 February 1999; Revised 20 September 1999

Copyright © 2001 G. A. Kamenskii and Ju. P. Zabrodina. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is to consider the problem of extremum of the nonlocal functional, which depends on a function u(t,s) and its derivative with respect to t at several values of s. For this problem the generalized Weierstrass inequality, the principle of minimum and the generalized conditions of Weierstrass–Erdmann are derived.