Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 696101 | https://doi.org/10.1155/S1085337504310031

Riccardo Molle, Donato Passaseo, "A finite-dimensional reduction method for slightly supercritical elliptic problems", Abstract and Applied Analysis, vol. 2004, Article ID 696101, 7 pages, 2004. https://doi.org/10.1155/S1085337504310031

A finite-dimensional reduction method for slightly supercritical elliptic problems

Received27 Aug 2003

Abstract

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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