Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights
Using the potential theory, we establish the existence and the asypmtotic behavior of radial solutions for the following boundaryvalue problem:\begin{equation*}\left\{\begin{aligned}&-\dfrac{1}{A}(A\phi(\mid u' \mid) u')'=a(t)u^\sigma & \mbox{on } (0,1),\\&A \p...
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| Дата: | 2024 |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1064 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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oai:jmag.ilt.kharkiv.ua:article-10642024-12-10T20:10:43Z Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights Belkahla, Sywar Khamessi, Bilel Zine El Abidine, Zagharide додатнi розв’язки асимптотична поведiнка φ-лапласiан клас Карамати positive solutions asymptotic behavior φ-Laplacian Karamata class Using the potential theory, we establish the existence and the asypmtotic behavior of radial solutions for the following boundaryvalue problem:\begin{equation*}\left\{\begin{aligned}&-\dfrac{1}{A}(A\phi(\mid u' \mid) u')'=a(t)u^\sigma & \mbox{on } (0,1),\\&A \phi(\mid u'\mid )u'(0)=0, \\&u(1)=0,\end{aligned}\right.\end{equation*}where $\sigma>0$, $A$ is a positive differentiable function on $(0,1)$ and the nonnegative function $\phi$ is continuously differentiable on $[0,\infty)$ such that for each $t>0$, $$ k_1 \le \dfrac{(t\phi(t))'}{\phi(t)} \le k_2, $$ where $k_1>0$ and $k_2>0$. The nonnegative nonlinearity $a$ is required to satisfy some appropriate assumptions related to the Karamata regular variation theory. We end this paper by giving applications. Mathematical Subject Classification 2020: 26A12, 34A34, 34B15, 34B18, 34B27 Використовуючи теорiю потенцiалу, встановлюємо iснування та асимптотичну поведiнку радiальних розв’язкiв наступної крайової задачі: \begin{equation*}\left\{\begin{aligned}&-\dfrac{1}{A}(A\phi(\mid u' \mid) u')'=a(t)u^\sigma & \mbox{on } (0,1),\\&A \phi(\mid u'\mid )u'(0)=0, \\&u(1)=0,\end{aligned}\right.\end{equation*}де $\sigma>0$, $A$ є додатною диференційовною функцією на $(0,1)$, а невід’ємна функція $\phi$ є неперервно диференційовною на $[0,\infty)$ так, що для кожного $t>0$, $$k_1 \le \dfrac{(t\phi(t))'}{\phi(t)} \le k_2,$$ де $k_1>0$ і $k_2>0$. Невід'ємна нелінійність $a$ повинна задовольняти деякі відповідні припущення, пов’язані з теорією регулярних варіацій Карамати. Ми закінчуємо цю роботу розглядом застосувань. Mathematical Subject Classification 2020: 26A12, 34A34, 34B15, 34B18, 34B27 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2024-06-29 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1064 10.15407/mag20.02.153 Journal of Mathematical Physics, Analysis, Geometry; Vol. 20 No. 2 (2024); 153–171 Журнал математической физики, анализа, геометрии; Том 20 № 2 (2024); 153–171 Журнал математичної фізики, аналізу, геометрії; Том 20 № 2 (2024); 153–171 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1064/jm20-0153e |
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Journal of Mathematical Physics, Analysis, Geometry |
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| datestamp_date |
2024-12-10T20:10:43Z |
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OJS |
| language |
English |
| topic |
додатнi розв’язки асимптотична поведiнка φ-лапласiан клас Карамати |
| spellingShingle |
додатнi розв’язки асимптотична поведiнка φ-лапласiан клас Карамати Belkahla, Sywar Khamessi, Bilel Zine El Abidine, Zagharide Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| topic_facet |
додатнi розв’язки асимптотична поведiнка φ-лапласiан клас Карамати positive solutions asymptotic behavior φ-Laplacian Karamata class |
| format |
Article |
| author |
Belkahla, Sywar Khamessi, Bilel Zine El Abidine, Zagharide |
| author_facet |
Belkahla, Sywar Khamessi, Bilel Zine El Abidine, Zagharide |
| author_sort |
Belkahla, Sywar |
| title |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| title_short |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| title_full |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| title_fullStr |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| title_full_unstemmed |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| title_sort |
radial positive solutions for problems involving φ-laplacian operators with weights |
| title_alt |
Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights Radial Positive Solutions for Problems Involving φ-Laplacian Operators with Weights |
| description |
Using the potential theory, we establish the existence and the asypmtotic behavior of radial solutions for the following boundaryvalue problem:\begin{equation*}\left\{\begin{aligned}&-\dfrac{1}{A}(A\phi(\mid u' \mid) u')'=a(t)u^\sigma & \mbox{on } (0,1),\\&A \phi(\mid u'\mid )u'(0)=0, \\&u(1)=0,\end{aligned}\right.\end{equation*}where $\sigma>0$, $A$ is a positive differentiable function on $(0,1)$ and the nonnegative function $\phi$ is continuously differentiable on $[0,\infty)$ such that for each $t>0$, $$ k_1 \le \dfrac{(t\phi(t))'}{\phi(t)} \le k_2, $$ where $k_1>0$ and $k_2>0$. The nonnegative nonlinearity $a$ is required to satisfy some appropriate assumptions related to the Karamata regular variation theory. We end this paper by giving applications.
Mathematical Subject Classification 2020: 26A12, 34A34, 34B15, 34B18, 34B27 |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| publishDate |
2024 |
| url |
https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1064 |
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AT belkahlasywar radialpositivesolutionsforproblemsinvolvingphlaplacianoperatorswithweights AT khamessibilel radialpositivesolutionsforproblemsinvolvingphlaplacianoperatorswithweights AT zineelabidinezagharide radialpositivesolutionsforproblemsinvolvingphlaplacianoperatorswithweights |
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2025-09-26T01:40:43Z |
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2025-09-26T01:40:43Z |
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