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Subelliptic and parametric equations on Carnot groups

Authors: Giovanni Molica Bisci and Massimiliano Ferrara
Journal: Proc. Amer. Math. Soc. 144 (2016), 3035-3045
MSC (2010): Primary 35J65; Secondary 22E25
Published electronically: November 6, 2015
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Abstract: 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.

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Giovanni Molica Bisci
Affiliation: Dipartimento P.A.U., Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari - Feo di Vito, 89100 Reggio, Calabria, Italy

Massimiliano Ferrara
Affiliation: University of Reggio Calabria and CRIOS University Bocconi of Milan, Via dei Bianchi presso Palazzo Zani, 89127 Reggio, Calabria, Italy

Keywords: Subelliptic equations, Carnot groups, multiple solutions, critical point results
Received by editor(s): May 10, 2015
Received by editor(s) in revised form: August 17, 2015, and September 3, 2015
Published electronically: November 6, 2015
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2015 American Mathematical Society