Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent
In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t \phi = u^2, \quad \text{in } \mathbb{R}^3, }$$ where $s\in(0,3/4)$, $t\in(0...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/01/abstr.html |
| Summary: | In this article we consider the fractional Schrodinger-Poisson system
$$\displaylines{
(-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u
= |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr
(-\Delta)^t \phi = u^2, \quad \text{in } \mathbb{R}^3,
}$$
where $s\in(0,3/4)$, $t\in(0,1)$, $2t+4s=3$, $\lambda>0$
and $2^*_s=6/(3-2s)$ is the Sobolev critical exponent.
By using perturbation method, we establish the existence of a solution for
$\lambda$ small enough. |
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| ISSN: | 1072-6691 |