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.
Keywords:
Bohl theorem, bounded solution, symbol of equation, representation of a bounded solution.
Citation:
E. Mukhamadiev, A. N. Naimov, A. Kh. Sattorov, “Analogue of Bohl theorem for a class of linear partial differential equations”, Ufa Math. J., 9:1 (2017), 75–88
\Bibitem{MuhNaiSat17}
\by E.~Mukhamadiev, A.~N.~Naimov, A.~Kh.~Sattorov
\paper Analogue of Bohl theorem for a~class of linear partial differential equations
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 1
\pages 75--88
\mathnet{http://mi.mathnet.ru/eng/ufa367}
\crossref{https://doi.org/10.13108/2017-9-1-75}
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Linking options:
https://www.mathnet.ru/eng/ufa367
https://doi.org/10.13108/2017-9-1-75
https://www.mathnet.ru/eng/ufa/v9/i1/p75
This publication is cited in the following 2 articles:
M. M. Kobilzoda, A. N. Naimov, “Ob ogranichennykh resheniyakh odnogo klassa sistem obyknovennykh differentsialnykh uravnenii”, Materialy Voronezhskoi vesennei matematicheskoi shkoly
«Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 3, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 192, VINITI RAN, M., 2021, 65–73
A. G. Baskakov, E. E. Dikarev, “Spectral theory of functions in studying partial differential operators”, Ufa Math. J., 11:1 (2019), 3–18
Citation in format AMSBIB
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