Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 179-196.

Critical Dirichlet problems on H domains of Carnot groups

Giovanni Molica Bisci, Patrizia Pucci

The paper deals with the existence of at least one (weak) solution for a wide class of one-parameter subelliptic critical problems in unbounded domains $\Omega$ of a Carnot group $\mathbb{G}$, which present several difficulties, due to the intrinsic lack of compactness. More precisely, when the real parameter is sufficiently small, thanks to the celebrated symmetric criticality principle of Palais, we are able to show the existence of at least one nontrivial solution. The proof techniques are based on variational arguments and on a recent compactness result, due to Balogh and Kristaly in [2]. In contrast with a persisting assumption in the current literature we do not require any longer the strongly asymptotically contractive condition on the domain $\Omega$. A direct application of the main result in the meaningful subcase of the Heisenberg group is also presented.

Published September 15, 2018.
Math Subject Classifications: 35R03, 35A15.
Key Words: Carnot groups; compactness results; subelliptic critical equations.

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Giovanni Molica Bisci
Department Patrimonio, Architettura, Urbanistica (PAU)
Università Mediterranea di Reggio Calabria
Via Graziella, Feo di Vito 89124, Reggio Calabria, Italy
Patrizia Pucci
Department of Mathematics and Informatics
University of Perugia, Via Vanvitelli, 1
06123 Perugia, Italy

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