Electron. J. Differential Equations, Vol. 2025 (2025), No. 46, pp. 1-8.
Nonlocal critical Kirchhoff problems in high dimension
Giovanni Anello
Abstract:
We study the nonlocal critical Kirchhoff problem
where is a bounded smooth domain in , , ,
, is the critical exponent for the
Sobolev embedding, and is a
Caratheodory function with subcritical growth. We establish the
existence of global minimizers for the energy functional associated to
this problem. In particular, we improve a recent result proved by Faraci
and Silva [3] under more strict conditions on the nonlinearity f
and under additional conditions on a and b.
Submitted January 27, 2025. Published May 6, 2025.
Math Subject Classifications: 35J20, 35J25.
Key Words: Nonlocal problem; Kirchhoff equation; weak solution; critical growth;
approximation; variational methods.
DOI: 10.58997/ejde.2025.46
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Giovanni Anello
Department of Mathematics and Computer Science
Physical Science and Earth Science
University of Messina
Viale F. Stagno d'Alcontres 31, Italy
email: ganello@unime.it
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