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      Existence of PrescribedL2-Norm Solutions for a Class of Schrödinger-Poisson Equation

      , ,
      Abstract and Applied Analysis
      Hindawi Limited

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          Abstract

          By using the standard scaling arguments, we show that the infimum of the following minimization problem: Iρ2=inf{(1/2)3|u|2dx+(1/4)3(|u(x)|2|u(y)|2/|x-y|)dxdy(1/p)3|u|pdx:uBρ}can be achieved for p(2,3)and ρ>0small, where Bρ:={uH1(3):u2=ρ}. Moreover, the properties of Iρ2/ρ2and the associated Lagrange multiplier λρare also given if p(2,8/3].

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          Most cited references18

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          The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. * *Mp denotes the Marcinkiewicz space or weak Lp space

          P.L. Lions (1984)
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            The concentration-compactness principle in the Calculus of Variations. The Locally compact case, part 2

            P.L. Lions (1984)
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              The Schrödinger–Poisson equation under the effect of a nonlinear local term

              David Ruiz (2006)
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                Author and article information

                Journal
                Abstract and Applied Analysis
                Abstract and Applied Analysis
                Hindawi Limited
                1085-3375
                1687-0409
                2013
                2013
                : 2013
                :
                : 1-11
                Article
                10.1155/2013/398164
                53b5fff8-a400-4d6b-abc0-e2d3ef4b788b
                © 2013

                http://creativecommons.org/licenses/by/3.0/

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