Geodesic
Existence of a solution to the nonhomogeneous ultrahyperbolic equation
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 77-100

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The nonhomogeneous ultrahyperbolic equation in ${\mathbb R}^d\times{\mathbb R}^n$ is considered. An additional condition prescribing the behavior of a solution to the equation at the infinity is proposed. It is proved that the problem for the equation in consideration with such a condition is not overdetermined. The solution is given in a form of a singular integral, and the corresponding asymptotics is found with the use of the stationary phase method. 
@article{ZNSL_2024_533_a4,
     author = {M. N. Demchenko},
     title = {Existence of a solution to the nonhomogeneous ultrahyperbolic equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--100},
     publisher = {mathdoc},
     volume = {533},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_533_a4/}
}
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M. N. Demchenko. Existence of a solution to the nonhomogeneous ultrahyperbolic equation. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 54, Tome 533 (2024), pp. 77-100. http://geodesic.mathdoc.fr/item/ZNSL_2024_533_a4/