Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas

TL;DR

This paper constructs solutions with two opposite-signed peaks for a plasma-related elliptic free boundary problem, analyzing their qualitative properties and peak locations as a parameter approaches zero.

Contribution

It introduces a perturbative method to find two-peak solutions with opposite signs in a plasma model, revealing new qualitative behaviors.

Findings

Solutions have two opposite-signed peaks at specified levels.

Level sets of solutions are connected.

Peak locations asymptotically approach certain positions as gamma tends to zero.

Abstract

By a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels $1$ and $-\gamma$, respectively, where $0<\gamma<1$. We establish some physically relevant qualitative properties for such solutions, including the connectedness of the level sets and the asymptotic location of the peaks as $\gamma\to0^+$.