Existence of solutions of some equations with advanced argument
by
Antoni Augustynowicz
Gdańsk University, Institute of Mathematics

The Cauchy problem for equation

x'(t)=f(t, x(h(t)))+g(t, x(t))

and the Darboux problem for

uxy(x, y)=F(x, y, u(H(x, y)))+G(x, y, u(x, y))

on unbounded domains are considered. Without assumption that h and H are delays, the existence of solutions and extremal solutions is obtained. We considered also equations with the Hale operator and hyperbolic equations with the right-hand side depending on the first order partial derivatives.

Date received: March 30, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canu-93.