Abstract. In the present paper, the existence, uniqueness and continuous dependence upon the data of the strong solution of a mixed problem for a singular second order hyperbolic equation with an integral condition is proved. The proof is essentially based on an a priori estimate and on the density of the range of the operator generated by the considered problem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. The investigation is accomplished in a traditional functional analysis language and techniques.

AMS Subject Classification (1991): 35L20, 35L67

Keyword(s): Singular hyperbolic equation, Integral condition, Strong solution

Received January 3, 2001, and in revised form March 6, 2003. (Registered under 5799/2009.)