Journal of Applied Mathematics 
Volume 1 (2001), Issue 3, Pages 107-116
doi:10.1155/S1110757X01000365

Mixed problem with integral conditions for a certain class of hyperbolic equations

Said Mesloub1 and Abdelfatah Bouziani2

 1Department of Mathematics, University of Tebessa, Tebessa 12002, Algeria
2Department of Mathematics, University of Oum El Bouaghi, BP 565, 04000, Algeria
Received 23 May 2001

Abstract

We study a mixed problem with purely integral conditions for a class of two-dimensional second-order hyperbolic equations. We prove the existence, uniqueness, and the continuous dependence upon the data of a generalized solution. We use a functional analysis method based on a priori estimate and on the density of the range of the operator generated by the considered problem.