A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions

2025/08/03 by Bartolucci, Daniele, Hu, Yeyao, Jevnikar, Aleks +2 · 1 citation
#35B30 #35B32 #35J57 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.01849

Abstract

We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, we prove uniqueness of positive solutions in a suitable interval and show that the associated energies and boundary values have a monotonic behavior. Some consequences are discussed about the parametrization of the unbounded Rabinowitz continuum for a class of superlinear strongly coupled elliptic systems.

Citations

• Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
• Global bifurcation analysis of mean field equations and the Onsager\n microcanonical description of two-dimensional turbulence
• A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma

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