Affiliation:
1. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, China. E-mails: zhangypzn@163.com, youpei.zhang@inf.ucv.ro
2. Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, Craiova 200585, Romania
Abstract
We are concerned with the mathematical and asymptotic analysis of solutions to the following nonlinear problem − Δ A u = λ β ( x ) | u | q u + f ( | u | ) u in Ω , u = 0 on ∂ Ω , where Δ A u is the magnetic Laplace operator, Ω ⊂ R N is a smooth bounded domain, A : Ω ↦ R N is the magnetic potential, u : Ω ↦ C, λ is a real parameter, β ∈ L ∞ ( Ω , R ) is an indefinite potential, q is nonnegative, and f : [ 0 , + ∞ ) ↦ R is a reaction that oscillates either in a neighborhood of the origin or at infinity. We analyze two distinct cases, in close relationship with the oscillatory growth of the reaction. Additionally, we give asymptotic estimates for the norm of the solutions in related function spaces.
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