On extremal solutions of differential equations with advanced argument

ArticleOriginal scientific text

Title

Authors ,

We obtain existence of absolutely continuous extremal solutions of the problem

u^{'} (x) = F (x, u (x), u (h (x)))

,

u (0) = u_{0}

, and the Darboux problem for

u_{x y} (x, y) = G (x, y, u (x, y), u (H (x, y)))

, where

h

and

H

are arbitrary continuous deviated arguments.

functional differential equations, advanced argument, extremal solutions, Darboux problem, Carathéodory condition