On the compactness threshold in the critical Kirchhoff equation

Erisa Hasani; Kanishka Perera

doi:10.3934/dcds.2021106

Article Contents

2022, Volume 42, Issue 1: 1-19. Doi: 10.3934/dcds.2021106

This issue Previous Article Next Article On the number of positive solutions to an indefinite parameter-dependent Neumann problem

On the compactness threshold in the critical Kirchhoff equation

Erisa Hasani and
Kanishka Perera^,

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

^*Corresponding author: Kanishka Perera
^*Corresponding author: Kanishka Perera

Received: November 30, 2020

Revised: April 30, 2021

Early access: July 2021

Published: January 2022

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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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Mathematics Subject Classification: Primary: 35J60; Secondary: 35B33, 35J20.

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