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Эта публикация цитируется в 14 научных статьях (всего в 14 статьях)
Analog of Hayman's theorem and its application to some system of linear partial differential equations
Andriy Banduraa, Oleh Skaskivb a Ivano-Frankivsk National Technical University of Oil and Gas, 15 Karpatska Str., Ivano-Frankivsk, 76019, Ukraine
b Ivan Franko National University of Lviv, 1 Universytetska Str., Lviv, 79000, Ukraine
Аннотация:
We used the analog of known Hayman's theorem to study the boundedness of $\mathbf{L}$-index in joint variables of entire solutions of some linear higher-order systems of PDE's and found sufficient conditions providing the boundedness, where $\mathbf{L}(z)=(l_1(z), \ldots, l_{n}(z)),$ $l_j:\mathbb{C}^n\to \mathbb{R}_+$ is a continuous function $j\in\{1,\ldots,n\}.$ Growth estimates of these solutions are also obtained. We proposed the examples of systems of PDE's which prove the exactness of these estimates for entire solutions. The obtained results are new even for the one-dimensional case because of the weakened restrictions imposed on the positive continuous function $l.$
Ключевые слова и фразы:
entire function, bounded $\mathbf{L}$-index in joint variables, linear higher-order systems of PDE, analytic theory of PDE, entire solution, linear higher-order differential equation.
Поступила в редакцию: 28.10.2017 Исправленный вариант: 06.11.2017
Образец цитирования:
Andriy Bandura, Oleh Skaskiv, “Analog of Hayman's theorem and its application to some system of linear partial differential equations”, Журн. матем. физ., анал., геом., 15:2 (2019), 170–191
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag721 https://www.mathnet.ru/rus/jmag/v15/i2/p170
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Страница аннотации: | 116 | PDF полного текста: | 52 | Список литературы: | 25 |
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