Aim of this paper is to study an elliptic equation driven by a general non-local integrodifferential operator and depending on a real parameter, in an open bounded set with Lipschitz boundary. In this framework, in the existence result proved along the paper, we show that our problem admits a non-trivial solution for any positive parameter provided it is different from the eigenvalues of the non-local operator. This result may be read as the non-local fractional counterpart of the one obtained by Capozzi, Fortunato and Palmieri and by Gazzola and Ruf for the classical Laplace equation with critical nonlinearities. In this sense the present work may be seen as the extension of some classical results for the Laplacian to the case of non-local fractional operators.
The Yamabe equation in a non-local setting
SERVADEI, RAFFAELLA
2013
Abstract
Aim of this paper is to study an elliptic equation driven by a general non-local integrodifferential operator and depending on a real parameter, in an open bounded set with Lipschitz boundary. In this framework, in the existence result proved along the paper, we show that our problem admits a non-trivial solution for any positive parameter provided it is different from the eigenvalues of the non-local operator. This result may be read as the non-local fractional counterpart of the one obtained by Capozzi, Fortunato and Palmieri and by Gazzola and Ruf for the classical Laplace equation with critical nonlinearities. In this sense the present work may be seen as the extension of some classical results for the Laplacian to the case of non-local fractional operators.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
