Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions
Analogues of the well known in the theory of analytic functions Phragmén — Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form di...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7843 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512788742406144 |
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| author | Kurta , V. V. Курта , В. В. |
| author_facet | Kurta , V. V. Курта , В. В. |
| author_sort | Kurta , V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-09-27T12:27:08Z |
| description | Analogues of the well known in the theory of analytic functions Phragmén — Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div (|∇и|α-2∇и) = f (х, и), where the function f(x, u) is locally bounded in ℝn+1,
f (х, 0) = 0, uf (х, и) ≥ а|и|1+q, а > 0, α > 1, α – 1 > q ≥ 0, n ≥ 2. |
| first_indexed | 2026-03-24T03:34:21Z |
| format | Article |
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| id | umjimathkievua-article-7843 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:34:21Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8d/91c5ebefce14ebc0b0fde7e6b50baf8d.pdf |
| spelling | umjimathkievua-article-78432023-09-27T12:27:08Z Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions О поведении решений квазилинейных эллиптических уравнений второго порядка в неограниченных областях Kurta , V. V. Курта , В. В. Analogues of the well known in the theory of analytic functions Phragmén — Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div (|∇и|α-2∇и) = f (х, и), where the function f(x, u) is locally bounded in ℝn+1, f (х, 0) = 0, uf (х, и) ≥ а|и|1+q, а > 0, α > 1, α – 1 > q ≥ 0, n ≥ 2. Сформулированы аналоги известной в теории аналитических функций теоремы Фрагмена — Линделефа для решений широкого класса квазилинейных уравнений эллиптического типа. Приведены примеры, иллюстрирующие точность полученных результатов для решений уравнения вида div (|∇и|α-2∇и) = f (х, и), где f (х, и) — локально ограниченная в ℝn+1 функция, f (х, 0) = 0, uf (х, и) ≥ а|и|1+q, а > 0, α > 1, α – 1 > q ≥ 0, n ≥ 2. Сформульовані аналоги відомої в теорії аналітичних функцій теореми Фрагмена — Лінделефа для розв’язків широкого класу квазілінійних рівнянь еліптичного типу. Наведені приклади, що ілюструють точність одержаних результатів для розв’язків рівняння вигляду div (|∇и|α-2∇и) = f (х, и), де f (х, и) — локально обмежена в ℝn+1 функція, f (х, 0) = 0, uf (х, и) ≥ а|и|1+q, а > 0, α > 1, α – 1 > q ≥ 0, n ≥ 2. Institute of Mathematics, NAS of Ukraine 1992-02-28 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7843 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 2 (1992); 279-283 Український математичний журнал; Том 44 № 2 (1992); 279-283 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7843/9492 Copyright (c) 1992 V. V. Kurta |
| spellingShingle | Kurta , V. V. Курта , В. В. Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title | Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title_alt | О поведении решений квазилинейных эллиптических уравнений второго порядка в неограниченных областях |
| title_full | Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title_fullStr | Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title_full_unstemmed | Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title_short | Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| title_sort | behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7843 |
| work_keys_str_mv | AT kurtavv behaviourofsolutionsofquasilinearellipticalequationsofthesecondorderinnonrestrictedregions AT kurtavv behaviourofsolutionsofquasilinearellipticalequationsofthesecondorderinnonrestrictedregions AT kurtavv opovedeniirešenijkvazilinejnyhélliptičeskihuravnenijvtorogoporâdkavneograničennyhoblastâh AT kurtavv opovedeniirešenijkvazilinejnyhélliptičeskihuravnenijvtorogoporâdkavneograničennyhoblastâh |