On a critical Kirchhoff-type problem

In the present paper we study a Kirchhoff type problem involving the critical Sobolev exponent. We give sufficient conditions for the sequentially weakly lower semicontinuity and the Palais–Smale property of the energy functional associated to the problem.

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Bibliographic Details
Published in:Nonlinear analysis 2020-03, Vol.192, p.111679, Article 111679
Main Authors: Faraci, Francesca, Farkas, Csaba
Format: Article
Language:English
Subjects:
Critical nonlinearity
Exterior domains
Kirchhoff type problem
Palais–Smale condition
Sequentially weakly lower semicontinuity
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Summary:In the present paper we study a Kirchhoff type problem involving the critical Sobolev exponent. We give sufficient conditions for the sequentially weakly lower semicontinuity and the Palais–Smale property of the energy functional associated to the problem.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.111679