Existence of Prescribed L2‐Norm Solutions for a Class of Schrödinger‐Poisson Equation

Yisheng Huang, Zeng Liu and Yuanze Wu

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf {(1/2)∫ℝ3 |∇u|2dx+(14/)∬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 and the associated Lagrange multiplier λρ are also given if p ∈ (2,8/3].

Date: 2013
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https://doi.org/10.1155/2013/398164

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:398164

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