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**The existence of a solution of a nonhomogeneous partial derivative equation in a class of functions that are increasing no faster than the polynomial.**
*(English.
Russian original)*
Zbl 0609.35089

Sov. Math. 30, No. 2, 92-96 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 2(285), 64-67 (1986).

The author considers a nonhomogeneous partial differential equation in two variables defined by a differential polynomial. He proves many results about the solutions of the given partial differential equation in a class M of infinitely differentiable functions that are bounded by polynomials. It is proved that the equation has a solution in M. Necessary and sufficient conditions for the existence of a finite number of linearly independent solutions of the corresponding homogeneous equation are established. The paper also contains estimates for the solutions of a problem associated to the homogeneous equation.

Reviewer: D.Ştefănescu

### MSC:

35S15 | Boundary value problems for PDEs with pseudodifferential operators |

35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |

35B65 | Smoothness and regularity of solutions to PDEs |