Journal of Inequalities and Applications 
Volume 6 (2001), Issue 1, Pages 17-27
doi:10.1155/S1025583401000029

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

Abstract

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.