Abstract and Applied Analysis
Volume 2004 (2004), Issue 8, Pages 683-689
A finite-dimensional reduction method for slightly supercritical elliptic problems
1Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, Roma 1, 00133, Italy
2Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, P.O. Box 193, Lecce 73100, Italy
Received 27 August 2003
Copyright © 2004 Riccardo Molle and Donato Passaseo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 the 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.