Existence of Prescribed L2-Norm Solutions for a Class of Schrödinger-Poisson Equation
By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)∫ℝ3|∇u|2dx+(1/4)∬ℝ3(|u(x)|2|u(y)|2/|x-y|)dx dy − (1/p)∫ℝ3|u|pdx:u∈Bρ} can be achieved for p∈(2,3) and ρ>0 small, where Bρ:={u∈H1(ℝ3):∥u∥2=ρ}. Moreover, the properties of Iρ2/ρ2 a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/398164 |