Title: Solutions for singular critical growth Schrödinger equations with magnetic field.
Abstract: In this paper, we are concerned with the semilinear Schrodinger equation (1.1) −∆Au− V (x)u = |u| ∗−2u , x ∈ R , where −∆A = (−i∇+A)2, u : R → C, N ≥ 3, 2∗ = 2N N−2 denotes the critical Sobolev exponent, A = (A1, A2, ..., AN ) : R N → R is the vector (or magnetic) potential, the coefficient V is the scalar (or electric) potential and may be signchanging. The nonlinear Schrodinger equation arises in different physical theories (e.g., the description of Bose–Estein condensates and nonlinear optics), and has been widely considered in the literature, see [1, 6, 7, 8, 11, 13]. Throughout this paper, suppose A ∈ Lloc(R ,R ). Define L(R , V −dx) := {
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
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Cited By Count: 1
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