Positive Solutions of a Nonlinear Elliptic Equation Involving a Singular Term
In this work, we study the existence and uniqueness of positive solutions to the equation $\Delta_p\, u=f(\vert x \vert)/u(x)$, $x\in \mathbb{R}^{N}$, where $N > p > 2$. More precisely, under certain assumptions concerning the function $f$, we provide an answer to the question of globa...
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| Datum: | 2025 |
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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
2025
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1098 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | In this work, we study the existence and uniqueness of positive solutions to the equation $\Delta_p\, u=f(\vert x \vert)/u(x)$, $x\in \mathbb{R}^{N}$, where $N > p > 2$. More precisely, under certain assumptions concerning the function $f$, we provide an answer to the question of global existence formulated in [14] by using the theory of invariant manifolds in dynamical systems and the energy method. In addition, we perform a detailed analysis of the asymptotic behavior of solutions by using logarithmic transformations.
Mathematical Subject Classification 2020: 35A01, 35A02, 35B08, 35B09, 35B40, 35J60, 35J65 |
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