Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 2, Pages 125-140
doi:10.1155/S1048953302000138

On a class of nonclassical hyperbolic equations with nonlocal conditions

Abdelfatah Bouziani

Centre Universitaire d'Oum El Baouagui, Département de Mathématiques, B.P. 565, Oum El Baouagui 04000, Algeria

Received 1 January 1998; Revised 1 September 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract formulation of the considered problem.