In this paper we complete the study of a critical elliptic equation, driven by a general non-local integrodifferential operator and depending on a real parameter, started by Servadei and Valdinoci (Commun Pure Appl Anal 12( 6): 24452464, 2013). Under suitable growth condition on the nonlinearity, we show that this problem admits non-trivial solutions for any positive parameter. This existence theorem extends some results obtained in previous papers by the same authors. In the model case, that is when the non-local operator is the fractional Laplacian, the existence result proved along the paper may be read as the non-local fractional counterpart of the one obtained in [12] (see also [9]) in the framework of the classical Laplace equation with critical nonlinearities.
Fractional Laplacian equations with critical Sobolev exponent
SERVADEI, RAFFAELLA;
2015
Abstract
In this paper we complete the study of a critical elliptic equation, driven by a general non-local integrodifferential operator and depending on a real parameter, started by Servadei and Valdinoci (Commun Pure Appl Anal 12( 6): 24452464, 2013). Under suitable growth condition on the nonlinearity, we show that this problem admits non-trivial solutions for any positive parameter. This existence theorem extends some results obtained in previous papers by the same authors. In the model case, that is when the non-local operator is the fractional Laplacian, the existence result proved along the paper may be read as the non-local fractional counterpart of the one obtained in [12] (see also [9]) in the framework of the classical Laplace equation with critical nonlinearities.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
