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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Статьи
Note on an eigenvalue problem for an ODE originating from a homogeneous $ p$-harmonic function
M. Akmana, J. Lewisb, A. Vogelc a Department of Mathematics, University of Connecticut, Storrs, CT 06269-3009
b Department of Mathematics, University of Kentucky, Lexington, KY 40506
c Department of Mathematics, Syracuse University, Syracuse, NY, 13244
Аннотация:
We discuss what is known about homogeneous solutions $ u$ to the $ p$-Laplace equation, $ p$ fixed, $ 10$ is $ p$-harmonic in the cone $\displaystyle K(\alpha )=\{x=(x_1,\dots , x_n) : x_1>\cos \alpha \vert x\vert\}\subset \mathbb{R}^n, n\geq 2,$ with continuous boundary value zero on $ \partial K(\alpha ) \setminus \{0\}$ when $ \alpha \in (0,\pi ]$. We also outline a proof of our new result concerning the exact value, $ \lambda =1-(n-1)/p$, for an eigenvalue problem in an ODE associated with $ u$ when $ u$ is $ p$ harmonic in $ K(\pi )$ and $ p>n-1$. Generalizations of this result are stated. Our result complements the work of Krol'-Maz'ya for $ 1<p\leq n-1$.
Ключевые слова:
$p$-Laplacian, boundary Harnack inequalities, homogeneous $p$-harmonic functions, eigenvalue problem.
Поступила в редакцию: 23.10.2018
Образец цитирования:
M. Akman, J. Lewis, A. Vogel, “Note on an eigenvalue problem for an ODE originating from a homogeneous $ p$-harmonic function”, Алгебра и анализ, 31:2 (2019), 75–87; St. Petersburg Math. J., 31:2 (2019), 241–250
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1638 https://www.mathnet.ru/rus/aa/v31/i2/p75
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Страница аннотации: | 288 | PDF полного текста: | 27 | Список литературы: | 39 | Первая страница: | 19 |
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