On weak solutions to a fractional Hardy–Hénon equation, Part II: Existence
نویسندگان
چکیده
This paper and [29] treat the existence nonexistence of stable weak solutions to a fractional Hardy--H\'enon equation $(-\Delta)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$, where $0 < s 1$, $\ell > -2s$, $p>1$, $N \geq 1$ 2s$. In this paper, when $p$ is critical or supercritical sense Joseph--Lundgren, we prove family positive radial solutions, which satisfies separation property. We also show multiple Joseph--Lundgren exponent for some \in (0,\infty)$ $s (0,1)$, property does not hold case $s=1$.
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ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2023
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2022.113165