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 |
| _version_ | 1818901246670536704 |
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| author | Tiankun Jin |
| author_facet | Tiankun Jin |
| author_sort | Tiankun Jin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T20:16:43Z |
| format | Article |
| id | doaj.art-84c35a75710f4bcaa3d365e265814024 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T20:16:43Z |
| publishDate | 2021-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-84c35a75710f4bcaa3d365e2658140242022-12-21T20:07:08ZengAIMS PressAIMS Mathematics2473-69882021-06-01689048905810.3934/math.2021525Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) conditionTiankun Jin0College of Teacher Education, Daqing Normal University, Daqing 163000, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/math.2021525?viewType=HTMLfractional schrödinger-poisson equationvariant fountain theoremvariational methods |
| spellingShingle | Tiankun Jin Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition AIMS Mathematics fractional schrödinger-poisson equation variant fountain theorem variational methods |
| title | Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition |
| title_full | Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition |
| title_fullStr | Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition |
| title_full_unstemmed | Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition |
| title_short | Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition |
| title_sort | multiplicity of solutions for a fractional schrodinger poisson system without ps condition |
| topic | fractional schrödinger-poisson equation variant fountain theorem variational methods |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021525?viewType=HTML |
| work_keys_str_mv | AT tiankunjin multiplicityofsolutionsforafractionalschrodingerpoissonsystemwithoutpscondition |