We study the nonlocal critical Kirchhoff problem (Formula Presented) where Ω is a bounded smooth domain in RN, N > 4, a, b > 0, λ ∈ R, (Formula Presented) is the critical N−2 exponent for the Sobolev embedding, and f: Ω × R → R is a Carathéodory 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.
Nonlocal critical Kirchhoff problems in high dimension
Anello, Giovanni
2025-01-01
Abstract
We study the nonlocal critical Kirchhoff problem (Formula Presented) where Ω is a bounded smooth domain in RN, N > 4, a, b > 0, λ ∈ R, (Formula Presented) is the critical N−2 exponent for the Sobolev embedding, and f: Ω × R → R is a Carathéodory 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.File in questo prodotto:
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