Geodesic
Inverse problem for Euler--Poisson--Darboux abstract differential equation
Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 126-141

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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. 
@article{CMFD_2006_15_a8,
     author = {A. V. Glushak and V. A. Popova},
     title = {Inverse problem for {Euler--Poisson--Darboux} abstract differential equation},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {126--141},
     publisher = {mathdoc},
     volume = {15},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/}
}
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A. V. Glushak; V. A. Popova. Inverse problem for Euler--Poisson--Darboux abstract differential equation. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, Tome 15 (2006), pp. 126-141. http://geodesic.mathdoc.fr/item/CMFD_2006_15_a8/