Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential

التفاصيل البيبلوغرافية
العنوان: Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
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 $n \geq 1$, $0-\lambda_{1,s}$, $20$ 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.
Comment: 11 pages
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2407.10126
رقم الأكسشن: edsarx.2407.10126
قاعدة البيانات: arXiv