On the compactness threshold in the critical Kirchhoff equation

2020/12/09 by Hasani, Erisa, Perera, Kanishka
#35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35J60 #Secondary 35B33

paper · doi:10.48550/arxiv.2012.05317

Abstract

We study a class of critical Kirchhoff problems with a general nonlocal term. The main difficulty here is the absence of a closed-form formula for the compactness threshold. First we obtain a variational characterization of this threshold level. Then we prove a series of existence and multiplicity results based on this variational characterization.

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