Open AccessSubelliptic and parametric equations on Carnot groups
Author(s) -
Giovanni Molica Bisci,
Массимилиано Феррара
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/12948
Subject(s) - carnot cycle , differentiable function , mathematics , class (philosophy) , parametric statistics , parametric equation , pure mathematics , mathematical analysis , computer science , physics , geometry , thermodynamics , statistics , artificial intelligence
This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for differentiable functionals due to Ricceri.