Geodesic
Analogue of Bohl theorem for a~class of linear partial differential equations
Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 75-88

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We study the existence and uniqueness of a solution bounded in the entire space for a class of higher order linear partial differential equations. We prove the theorem on the necessary and sufficient condition for the existence and uniqueness of a bounded solution for a studied class of equations. This theorem is an analogue of the Bohl theorem known in the theory of ordinary differential equations. In a partial case the unique solvability conditions are expressed in terms of the coefficients of the equation and we provide the integral representation for the bounded solution.
Keywords: Bohl theorem, bounded solution, representation of a bounded solution.
Mots-clés : symbol of equation 
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     title = {Analogue of {Bohl} theorem for a~class of linear partial differential equations},
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E. Mukhamadiev; A. N. Naimov; A. Kh. Sattorov. Analogue of Bohl theorem for a~class of linear partial differential equations. Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 75-88. http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a6/