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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/760157 |
| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |