International Journal of Mathematics and Mathematical Sciences 
Volume 22 (1999), Issue 3, Pages 511-519
doi:10.1155/S0161171299225112

On a class of singular hyperbolic equation with a weighted integral condition

Said Mesloub1 and Abdelfatah Bouziani2

1Département de Mathématiques, Centre Universitaire de Tebessa, 12000, Algeria
2Département de Mathématiques, Centre Universitaire d'Oum El Baouagui, BP. 565, 04000, Algeria

Received 15 June 1998

Abstract

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.