Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential
Abstract In this paper, we study the multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential. First, by using some ideas of the fountain theorem, we define a sequence of minimax values, and then we prove that these minimax values are c...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-11-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01968-7 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850129433130696704 |
|---|---|
| author | Xinsheng Du Shanshan Wang |
| author_facet | Xinsheng Du Shanshan Wang |
| author_sort | Xinsheng Du |
| collection | DOAJ |
| description | Abstract In this paper, we study the multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential. First, by using some ideas of the fountain theorem, we define a sequence of minimax values, and then we prove that these minimax values are critical values of the energy function restricted to a constraint set, which leads to the multiplicity of normalized solutions and extends some related results. |
| format | Article |
| id | doaj-art-45d85c3170be4e968777d9a1b442aebb |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-45d85c3170be4e968777d9a1b442aebb2025-08-20T02:33:00ZengSpringerOpenBoundary Value Problems1687-27702024-11-012024111510.1186/s13661-024-01968-7Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potentialXinsheng Du0Shanshan Wang1School of Mathematical Sciences, Qufu Normal UniversitySchool of Mathematical Sciences, Qufu Normal UniversityAbstract In this paper, we study the multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential. First, by using some ideas of the fountain theorem, we define a sequence of minimax values, and then we prove that these minimax values are critical values of the energy function restricted to a constraint set, which leads to the multiplicity of normalized solutions and extends some related results.https://doi.org/10.1186/s13661-024-01968-7Fractional Schrödinger–Poisson equationHardy potentialNormalized solutionMultiplicity |
| spellingShingle | Xinsheng Du Shanshan Wang Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential Boundary Value Problems Fractional Schrödinger–Poisson equation Hardy potential Normalized solution Multiplicity |
| title | Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential |
| title_full | Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential |
| title_fullStr | Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential |
| title_full_unstemmed | Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential |
| title_short | Multiplicity of normalized solutions to a class of nonlinear fractional Schrödinger–Poisson systems with Hardy potential |
| title_sort | multiplicity of normalized solutions to a class of nonlinear fractional schrodinger poisson systems with hardy potential |
| topic | Fractional Schrödinger–Poisson equation Hardy potential Normalized solution Multiplicity |
| url | https://doi.org/10.1186/s13661-024-01968-7 |
| work_keys_str_mv | AT xinshengdu multiplicityofnormalizedsolutionstoaclassofnonlinearfractionalschrodingerpoissonsystemswithhardypotential AT shanshanwang multiplicityofnormalizedsolutionstoaclassofnonlinearfractionalschrodingerpoissonsystemswithhardypotential |