Simplicity and boundary behavior of spike sequences for a superlinear problem in plasma physics

TL;DR

This paper proves that spike sequences in a plasma physics problem are simple and converge to interior points, refining previous blow-up analysis and establishing a converse to existing existence results.

Contribution

It establishes the simplicity and interior convergence of spike sequences, sharpening blow-up analysis and providing a converse to prior existence results in plasma physics.

Findings

Spike sequences are always simple.

Spike sequences converge toward interior points.

Refines previous blow-up analysis.

Abstract

We prove that spike sequences related to a nonlinear problem of Grad-Shafranov type are always simple and always converge toward interior points of the domain. This sharpens the blow-up analysis carried out by Bartolucci-Jevnikar-Wu [Calc. Var. 2025] and provides a converse to the existence result for spike sequences obtained by Wei [Proc. Edinb. Math. Soc. 2001].