A three-point boundary value problem with an integral condition for parabolic equations with the Bessel operator

In this paper, we study a three-point boundary value problem with an integral condition for a class of parabolic equation with Bessel operator. The existence and uniqueness of the solution in functional weighted Sobolev space are proved. The proof is based on two sided a priori estimates and the density of the range of the operator generated by the considered problem.