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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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7843 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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