The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method
Abstract This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to the problem because the quasilinear term makes it impossible to find a suitable spa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-10-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1272-3 |
| _version_ | 1819071287955292160 |
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| author | Lizhen Chen Xiaojing Feng Xinan Hao |
| author_facet | Lizhen Chen Xiaojing Feng Xinan Hao |
| author_sort | Lizhen Chen |
| collection | DOAJ |
| description | Abstract This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to the problem because the quasilinear term makes it impossible to find a suitable space in which the corresponding functional possesses both smoothness and compactness properties. In order to overcome the difficulties caused by nonlocal term and quasi-linear term, we shall apply the perturbation method by adding a 4-Laplacian operator to consider the perturbation problem. And then, by using the approximation technique, a sign-changing solution with precisely two nodal domains is derived. |
| first_indexed | 2024-12-21T17:19:27Z |
| format | Article |
| id | doaj.art-7c1264ce4dab47e0996d07787485354d |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-21T17:19:27Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-7c1264ce4dab47e0996d07787485354d2022-12-21T18:56:12ZengSpringerOpenBoundary Value Problems1687-27702019-10-012019111910.1186/s13661-019-1272-3The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation methodLizhen Chen0Xiaojing Feng1Xinan Hao2School of Applied Mathematics, Shanxi University of Finance and EconomicsSchool of Mathematical Sciences, Shanxi UniversitySchool of Mathematical Sciences, Qufu Normal UniversityAbstract This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to the problem because the quasilinear term makes it impossible to find a suitable space in which the corresponding functional possesses both smoothness and compactness properties. In order to overcome the difficulties caused by nonlocal term and quasi-linear term, we shall apply the perturbation method by adding a 4-Laplacian operator to consider the perturbation problem. And then, by using the approximation technique, a sign-changing solution with precisely two nodal domains is derived.http://link.springer.com/article/10.1186/s13661-019-1272-3Quasilinear Schrödinger–Poisson systemPerturbation methodSign-changing solution |
| spellingShingle | Lizhen Chen Xiaojing Feng Xinan Hao The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method Boundary Value Problems Quasilinear Schrödinger–Poisson system Perturbation method Sign-changing solution |
| title | The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method |
| title_full | The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method |
| title_fullStr | The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method |
| title_full_unstemmed | The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method |
| title_short | The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method |
| title_sort | existence of sign changing solution for a class of quasilinear schrodinger poisson systems via perturbation method |
| topic | Quasilinear Schrödinger–Poisson system Perturbation method Sign-changing solution |
| url | http://link.springer.com/article/10.1186/s13661-019-1272-3 |
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