تقرير
Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
العنوان: | Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential |
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المؤلفون: | Gou, Tianxiang, Radulescu, Vicentiu D. |
سنة النشر: | 2024 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35A02, 35R11 |
الوصف: | In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential \begin{align*} (-\Delta)^s u+ \left(\omega+|x|^2\right) u=|u|^{p-2}u \quad \mbox{in}\,\, \R^n, \end{align*} where $n \geq 1$, $0 0$ is the lowest eigenvalue of the operator $(-\Delta)^s + |x|^2$. This solves an open question raised in \cite{SS} concerning the uniqueness of solutions to the equation. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2407.10126 |
رقم الأكسشن: | edsarx.2407.10126 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |