A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Analysis of PDEs
2025-08-05 v1
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.
Cite
@article{arxiv.2508.01849,
title = {A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions},
author = {Daniele Bartolucci and Yeyao Hu and Aleks Jevnikar and Juncheng Wei and Wen Yang},
journal= {arXiv preprint arXiv:2508.01849},
year = {2025}
}
Comments
31 pages