Existence of Multiple Positive Solutions for Choquard Equation with Perturbation
This paper is concerned with the following Choquard equation with perturbation: -Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x), u∈H1(RN), where N≥3, α∈(0,N), and 2-(α/N)<p<(2N-α)/(N-2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions f...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/760157 |
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doaj-962763e6ad674f7db1d90180120f2a392021-07-02T02:00:42ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/760157760157Existence of Multiple Positive Solutions for Choquard Equation with PerturbationTao Xie0Lu Xiao1Jun Wang2School of Management, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaSchool of Management, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaFaculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaThis paper is concerned with the following Choquard equation with perturbation: -Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x), u∈H1(RN), where N≥3, α∈(0,N), and 2-(α/N)<p<(2N-α)/(N-2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functions V(x), we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation.http://dx.doi.org/10.1155/2015/760157 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tao Xie Lu Xiao Jun Wang |
| spellingShingle |
Tao Xie Lu Xiao Jun Wang Existence of Multiple Positive Solutions for Choquard Equation with Perturbation Advances in Mathematical Physics |
| author_facet |
Tao Xie Lu Xiao Jun Wang |
| author_sort |
Tao Xie |
| title |
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation |
| title_short |
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation |
| title_full |
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation |
| title_fullStr |
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation |
| title_full_unstemmed |
Existence of Multiple Positive Solutions for Choquard Equation with Perturbation |
| title_sort |
existence of multiple positive solutions for choquard equation with perturbation |
| publisher |
Hindawi Limited |
| series |
Advances in Mathematical Physics |
| issn |
1687-9120 1687-9139 |
| publishDate |
2015-01-01 |
| description |
This paper is concerned with the following Choquard equation with perturbation: -Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x), u∈H1(RN), where N≥3, α∈(0,N), and 2-(α/N)<p<(2N-α)/(N-2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functions V(x), we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation. |
| url |
http://dx.doi.org/10.1155/2015/760157 |
| work_keys_str_mv |
AT taoxie existenceofmultiplepositivesolutionsforchoquardequationwithperturbation AT luxiao existenceofmultiplepositivesolutionsforchoquardequationwithperturbation AT junwang existenceofmultiplepositivesolutionsforchoquardequationwithperturbation |
| _version_ |
1721343962058326016 |