Nonnegative solutions of the characteristic initial value problem for linear partial functional-differential equations of hyperbolic type

On the rectangle D = [a, b] x [c, d], the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation partial derivative(2)u(t,x)/partial derivative t partial derivative x = l(u)(t, x)+q(t, x) is considered, where l : C(D; R) -> L(D; R) is a linear bounded operator and q epsilon L(D; R+). (c) 2007 Elsevier Ltd. All rights reserved.