In this paper we describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.
A finite-dimensional reduction method for slightly supercritical elliptic problems
PASSASEO, Donato
2004-01-01
Abstract
In this paper we describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
