In this paper we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator, depending on a real parameter and with the nonlinear term which satisfies superlinear and subcritical growth conditions at zero and at infinity. This equation has a variational nature, and so its solutions can be found as critical points of the energy functional associated to the problem. Here we get such critical points using both the Mountain Pass Theorem and the Linking Theorem. As a particular case, we derive an existence theorem for an equation driven by the fractional Laplacian. Thus, the results presented here may be seen as the extension of some classical nonlinear analysis theorems to the case of fractional operators.
Variational methods for non-local operators of elliptic type
SERVADEI, RAFFAELLA;
2013
Abstract
In this paper we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator, depending on a real parameter and with the nonlinear term which satisfies superlinear and subcritical growth conditions at zero and at infinity. This equation has a variational nature, and so its solutions can be found as critical points of the energy functional associated to the problem. Here we get such critical points using both the Mountain Pass Theorem and the Linking Theorem. As a particular case, we derive an existence theorem for an equation driven by the fractional Laplacian. Thus, the results presented here may be seen as the extension of some classical nonlinear analysis theorems to the case of fractional operators.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
