Inverse Problems for a Three-dimensional Elliptic Equation for Finding the Right-hand Side with a Non-local Observation Condition

The article presents the formulation of inverse problems for a three-dimensional elliptic equation to find its right-hand side with an additional integral condition and substantiate their correctness in the Hadamard sense for the class of regular solutions. The uniqueness of the solutions to the problems is proved on the basis of integral identities. By the methods of separated variables and integral equations, the solutions of the problems are constructed explicitly and theorems of the existence and stability of solutions to the posed inverse problems are established.