Ufa Mathematical Journal
    Volume 9, Number 1, pp. 75-88

    Analogue of Bohl theorem for a class of linear partial differential equations

    Mukhamadiev E.M., Naimov A.N., Sattorov A.H.


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    We study the issue on 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.