Bounded solutions of a class of hyperbolic equations on the plane

Мухамадиев, Э. М.; Наимов, А. Н.; Sattorov, A. Kh.

doi:10.1134/s0012266116010079

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“…Theorems 2.2 and 2.3 for = 2 and 1 = 2 = 1 were proved in works [4], [5]. The monograph [6] provides results on exponential representation of generalized solutions to linear differential equations with constant coefficients.…”

Section: Resultsmentioning

confidence: 99%

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

Muhamadiev¹,

Наимов²,

Sattorov³

2017

Ufimskii Matematicheskii Zhurnal

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Abstract. 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.

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Section: Resultsmentioning

confidence: 99%