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.File in questo prodotto:
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