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 of a Carnot group 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 Kristály 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. A direct application of the main result in the meaningful subcase of the Heisenberg group is also presented.
Critical Dirichlet problems on H domains of Carnot groups
Molica Bisci G
;
2018
Abstract
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 of a Carnot group 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 Kristály 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. A direct application of the main result in the meaningful subcase of the Heisenberg group is also presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
