Author
Shengbin Yu
Bio: Shengbin Yu is an academic researcher from Fujian Normal University. The author has an hindex of 1, co-authored 1 publications receiving 1 citations.
Papers
More filters
••
TL;DR: In this paper, the existence, uniqueness, and monotonicity of positive solution uλ using the variational method were shown for fractional Schrodinger-Poisson systems with singularity under certain assumptions on V and f.
Abstract: In this paper, we consider the following fractional Schrodinger–Poisson system with singularity \begin{equation*}
\left \{\begin{array}{lcl} ({-}\Delta)^s u+V(x)u+\lambda \phi u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ ({-}\Delta)^t \phi = u^2, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3,
\end{array}\right.
\end{equation*} where 0 0 and 0 3. Under certain assumptions on V and f, we show the existence, uniqueness, and monotonicity of positive solution uλ using the variational method. We also give a convergence property of uλ as λ → 0, when λ is regarded as a positive parameter.
1 citations
Cited by
More filters
••
01 Jan 2021TL;DR: In this paper, the authors considered the following fractional Kirchhoff problem with singularity, where the singularity is the fractional Laplacian of the problem, and they considered the problem in terms of singularity.
Abstract: In this paper, we consider the following fractional Kirchhoff problem with singularity $ \left \{\begin{array}{lcl} \Big(1+ b\int_{\mathbb{R}^3}\int_{\mathbb{R}^3} \frac{|u(x)-u(y)|^2}{|x-y|^{3+2s}}\mathrm{d}x \mathrm{d}y \Big)(-\Delta)^s u+V(x)u = f(x)u^{-\gamma}, &&\quad x\in\mathbb{R}^3,\\ u>0,&&\quad x\in\mathbb{R}^3, \end{array}\right. $ where $ (-\Delta)^s $ is the fractional Laplacian with $ 0