Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells
The purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian (−Δ)psu(x)+λV(x)u(x)p−1=u(x)q−1,u(x)≥0,x∈RN,{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x)u{\left(x)}^{p-1}=u{\left(x)}^{q-1},\hspace{1e...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-03-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0006 |
| _version_ | 1828381339687059456 |
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| author | Chen Yongpeng Niu Miaomiao |
| author_facet | Chen Yongpeng Niu Miaomiao |
| author_sort | Chen Yongpeng |
| collection | DOAJ |
| description | The purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian (−Δ)psu(x)+λV(x)u(x)p−1=u(x)q−1,u(x)≥0,x∈RN,{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x)u{\left(x)}^{p-1}=u{\left(x)}^{q-1},\hspace{1em}u\left(x)\ge 0,\hspace{0.33em}x\in {{\mathbb{R}}}^{N}, where λ>0\lambda \gt 0 is a parameter, 1<p<q<NpN−sp1\lt p\lt q\lt \frac{Np}{N-sp}, N≥2N\ge 2, and V(x)V\left(x) is a real continuous function on RN{{\mathbb{R}}}^{N}. For λ\lambda large enough, the existence of ground state solutions are obtained, and they localize near the potential well int(V−1(0))\left({V}^{-1}\left(0)). |
| first_indexed | 2024-12-10T04:13:06Z |
| format | Article |
| id | doaj.art-3ecfb31fc02143d48b39604eef675409 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-10T04:13:06Z |
| publishDate | 2022-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-3ecfb31fc02143d48b39604eef6754092022-12-22T02:02:40ZengDe GruyterOpen Mathematics2391-54552022-03-01201506210.1515/math-2022-0006Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wellsChen Yongpeng0Niu Miaomiao1School of Science, Guangxi University of Science and Technology, Liuzhou, 545006, P. R. ChinaCollege of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, P. R. ChinaThe purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian (−Δ)psu(x)+λV(x)u(x)p−1=u(x)q−1,u(x)≥0,x∈RN,{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x)u{\left(x)}^{p-1}=u{\left(x)}^{q-1},\hspace{1em}u\left(x)\ge 0,\hspace{0.33em}x\in {{\mathbb{R}}}^{N}, where λ>0\lambda \gt 0 is a parameter, 1<p<q<NpN−sp1\lt p\lt q\lt \frac{Np}{N-sp}, N≥2N\ge 2, and V(x)V\left(x) is a real continuous function on RN{{\mathbb{R}}}^{N}. For λ\lambda large enough, the existence of ground state solutions are obtained, and they localize near the potential well int(V−1(0))\left({V}^{-1}\left(0)).https://doi.org/10.1515/math-2022-0006nonlinear schrödinger equationground state solutionfractional p-laplacianvariational methods35j6035b33 |
| spellingShingle | Chen Yongpeng Niu Miaomiao Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells Open Mathematics nonlinear schrödinger equation ground state solution fractional p-laplacian variational methods 35j60 35b33 |
| title | Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells |
| title_full | Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells |
| title_fullStr | Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells |
| title_full_unstemmed | Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells |
| title_short | Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells |
| title_sort | ground state solutions of nonlinear schrodinger equations involving the fractional p laplacian and potential wells |
| topic | nonlinear schrödinger equation ground state solution fractional p-laplacian variational methods 35j60 35b33 |
| url | https://doi.org/10.1515/math-2022-0006 |
| work_keys_str_mv | AT chenyongpeng groundstatesolutionsofnonlinearschrodingerequationsinvolvingthefractionalplaplacianandpotentialwells AT niumiaomiao groundstatesolutionsofnonlinearschrodingerequationsinvolvingthefractionalplaplacianandpotentialwells |