Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617772 | Journal of Mathematical Analysis and Applications | 2012 | 19 Pages |
Abstract
We study the existence of radially symmetric solutions u∈H1(Ω) of the following nonlinear scalar field equation −Δu=g(|x|,u) in Ω. Here Ω=RN or {x∈RN||x|>R}, N⩾2. We generalize the results of Li and Li (1993) [13], and Li (1990) [14] in which they studied the problem in RN and {|x|>R} with the Dirichlet boundary condition. Furthermore, we extend it to the Neumann boundary problem and we also consider the nonlinear Schrödinger equation that is the case .
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