PORTUGALIAE MATHEMATICA Vol. 63, No. 1, pp. 3745 (2006) 

Solutions for singular critical growth Schrödinger equations with magnetic fieldPigong HanInstitute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing 100080  PEOPLE'S REPUBLIC OF CHINA Email: 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 Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
