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

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE 2026 Open access

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Authors: Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar, Juncheng Wei, Wen Yang
DOI: 10.2422/2036-2145.202505_013
Cited by: 0

Abstract

We study a Hamiltonian system of free boundary type.We first establish uniform bounds and prove the existence of solutions as well as of the free boundary.Next, for any smooth and bounded domain, we prove uniqueness of positive solutions within 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 elliptic systems.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Nonlinear Differential Equations Analysis Contact Mechanics and Variational Inequalities

Publication details

Journal / source
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
Publisher
Scuola Normale Superiore - Edizioni della Normale
Pages
31–31
Publication date
25 June 2026
Language
EN