Existence and uniqueness of solutions in H1(Δ) of a general class of non-linear functional equations

A functional analytic method is used to prove the existence and the uniqueness of a solution in the Banach space H1(Δ) of a general class of non-linear functional equations. This general class includes some specific functional equations studied recently. Our results simplify and improve the existing results for these specific equations. Moreover, for one of them, we give an answer to an open problem.  2003 Elsevier Science (USA). All rights reserved