We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.
Abdelfatah Bouziani. "On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator." J. Appl. Math. 2003 (10) 487 - 502, 24 September 2003. https://doi.org/10.1155/S1110757X03204034