Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 1, pp. 37-45 (2006)

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Solutions for singular critical growth Schrödinger equations with magnetic field

Pigong Han

Institute of Applied Mathematics, Academy of Mathematics and Systems Science,
Chinese Academy of Sciences, Beijing 100080 -- PEOPLE'S REPUBLIC OF CHINA
E-mail: pghan@amss.ac.cn

Abstract: In this paper, we consider the semilinear stationary Schrödinger equation with a magnetic field: $-\Delta_A{u}-V(x)u=|u|^{2^*-2}u$ in $\R^N$, where $A$ is the vector (or magnetic) potential and $V$ is the scalar (or electric) potential. By means of variational method, we establish the existence of nontrivial solutions in the critical case.

Keywords: Schrödinger equation; energy functional; (P.S.) sequence; critical Sobolev exponent

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Electronic version published on: 7 Mar 2008.

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