Multiple solutions for a free boundary problem arising in plasma physics

Abstract

In this paper we study the existence of solutions for a free boundary problem arising in the study of the equilibrium of a plasma confined in a tokamak:where p > 2, Ω is a bounded domain in ℝ2, n is the outward unit normal of ∂Ω, α is an unprescribed constant and I is a given positive constant. The set Ω+ = {x ∊ Ω: u(x) > 0} is called a plasma set. Under the condition that the homology of Ω is non-trivial, we show that for any given integer k ≥ 1 there exists λk > 0 such that for λ > λk the problem above has a solution with a plasma set consisting of k components.