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Solution of perturbed Schrödinger system with critical nonlinearity and electromagnetic fields
Author(s) -
Zhang Huixing,
Liu Wenbin
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2550
Subject(s) - sobolev space , mathematics , nonlinear system , exponent , schrödinger's cat , critical exponent , energy (signal processing) , electromagnetic field , mathematical physics , mathematical analysis , physics , quantum mechanics , geometry , linguistics , philosophy , statistics , scaling
In this paper, we consider the following perturbed nonlinear Schrödinger system with electromagnetic fields−( ϵ ∇ + iA ( x ) )2 u + V ( x ) u = H s( | u | 2 , | v | 2) u + K ( x ) | u |2 蜧 − 2 u , x ∈ R N ,−( ϵ ∇ + iA ( x ) )2 v + V ( x ) v = H t( | u | 2 , | v | 2) v + K ( x ) | v |2 蜧 − 2 v , x ∈ R N ,where N ≥ 3, 2 蜧 = 2 N ∕ ( N − 2) is the Sobolev critical exponent; A is the real vector magnetic potential; and V ( x ), K ( x ), and H ( s , t ) are continuous functions. Under certain conditions on V , H , and K , we establish some new results on the existence of the least‐energy solutions ( u ϵ , v ϵ ) for small ϵ by using variational method. Copyright © 2012 John Wiley & Sons, Ltd.