On a class of nonclassical hyperbolic equations with nonlocal
conditions

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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

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.