Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition
In this paper, we study the following fractional Schrödinger-Poisson system $ \begin{equation*} \begin{cases} (-\Delta)^su+V(x)u+\phi u = f(x, u)& x\in\mathbb{R}^3, \\ (-\Delta)^s\phi = u^2& x\in\mathbb{R}^3. \end{cases} \end{equation*} $ Using the variant fountain theorem intr...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021525?viewType=HTML |
| Summary: | In this paper, we study the following fractional Schrödinger-Poisson system
$ \begin{equation*} \begin{cases} (-\Delta)^su+V(x)u+\phi u = f(x, u)& x\in\mathbb{R}^3, \\ (-\Delta)^s\phi = u^2& x\in\mathbb{R}^3. \end{cases} \end{equation*} $
Using the variant fountain theorem introduced by Zou <sup>[<xref ref-type="bibr" rid="b32">32</xref>]</sup>, we get the existence of infinitely many large energy solutions without the Ambrosetti-Rabinowitz's 4-superlinearity condition. Recent results from the literature are extended and improved. |
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| ISSN: | 2473-6988 |