Inverse problem for Euler-Poisson-Darboux abstract differential equation

For the nonhomogeneous Euler-Poisson-Darboux equation in a Banach space, we consider the problem of determination of a parameter on the right-hand side of the equation by the excessive final condition. This problem can be reduced to the inversion of some operator represented in a suitable form and related to the operator solving the Cauchy problem for the homogeneous Euler-Poisson-Darboux equation. As the final result, we show that the solvability of the problem considered depends on the distribution of zeroes of some analytic function. In addition, we give a simple sufficient condition ensuring the unique solvability of the problem. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 15, Differential and Functional Differential Equations. Part 1, 2006.