Multiplicity of solutions for the plasma problem in two dimensions

Author(s)
Cao, Daomin
Peng, Shuangjie
Yan, Shusen
Publication Date
2010
Abstract
Let Ω be a bounded domain in R², u+=u if u⩾0, u+=0 if u<0, u−=u+−u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma ... where ν is the outward unit normal of ∂Ω at x, c is a constant which is unprescribed, and I is a given positive constant. The set Ωp = {x ∈ Ω, u(x) < 0} is called plasma set. Existence of solutions whose plasma set consisting of one component and asymptotic behavior of plasma set were studied by Caffarelli and Friedman (1980) [3] for large λ. Under the condition that the homology of Ω is nontrivial we obtain in this paper by a constructive way that for any given integer k⩾1, there is λk>0 such that for λ>λk, (Pλ) has a solution with plasma set consisting of k components.
Citation
Advances in Mathematics, 225(5), p. 2741-2785
ISSN
1090-2082
0001-8708
Link
Publisher
Academic Press
Title
Multiplicity of solutions for the plasma problem in two dimensions
Type of document
Journal Article
Entity Type
Publication

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