We consider the Brezis-Nirenberg problem in a bounded domain Ω with nontrivial topology and smooth boundary and we prove the existence of a new type of positive and signchanging solution in a “subcritical” and in a “supercritical” setting. We remark that this is the first result of existence of a sign-changing solution in “the supercritical” case.

A new kind of blowing-up solutions for the Brezis-Nirenberg problem

VAIRA, Giusi
2015

Abstract

We consider the Brezis-Nirenberg problem in a bounded domain Ω with nontrivial topology and smooth boundary and we prove the existence of a new type of positive and signchanging solution in a “subcritical” and in a “supercritical” setting. We remark that this is the first result of existence of a sign-changing solution in “the supercritical” case.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/368446
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