In this paper we discuss the existence of infinitely many solutions for a nonlocal, nonlinear equation with homogeneous Dirichlet boundary data. Adapting the classical variational techniques used in order to study the standard Laplace equation with subcritical growth nonlinearities to the nonlocal framework, along the present paper we prove that this problem admits infinitely many weak solutions uk, with the property that their Sobolev norm goes to infinity, provided the exponent satisfies suitable assumptions. In this sense, the results presented here may be seen as the extension of some classical nonlinear analysis theorems to the case of fractional operators.
Infinitely many solutions for fractional Laplace equations with subcritical nonlinearity
SERVADEI, RAFFAELLA
2013
Abstract
In this paper we discuss the existence of infinitely many solutions for a nonlocal, nonlinear equation with homogeneous Dirichlet boundary data. Adapting the classical variational techniques used in order to study the standard Laplace equation with subcritical growth nonlinearities to the nonlocal framework, along the present paper we prove that this problem admits infinitely many weak solutions uk, with the property that their Sobolev norm goes to infinity, provided the exponent satisfies suitable assumptions. In this sense, 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.
