A finite‐dimensional reduction method for slightly supercritical elliptic problems

Riccardo Molle and Donato Passaseo

Abstract and Applied Analysis, 2004, vol. 2004, issue 8, 683-689

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.

Date: 2004
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https://doi.org/10.1155/S1085337504310031

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:8:p:683-689

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