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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| Datum: | 2024 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Online Zugang: | 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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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | 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 |
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