Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/355800
Type: Artigo
Title: A critical kirchhoff‐type problem driven by a p (·)‐fractional Laplace operator with variable s (·) ‐order
Author: Zuo, Jiabin
An, Tianqing
Fiscella, Alessio
Abstract: The paper deals with the following Kirchhoff‐type problem M ∬ ℝ 2 N 1 p ( x , y ) | v ( x ) − v ( y ) | p ( x , y ) | x − y | N + p ( x , y ) s ( x , y ) d x d y ( − Δ ) p ( · ) s ( · ) v ( x ) = μ g ( x , v ) + | v | r ( x ) − 2 v in Ω , v = 0 in ℝ N \ Ω , where M models a Kirchhoff coefficient, ( − Δ ) p ( · ) s ( · ) is a variable s(·)‐order p(·)‐fractional Laplace operator, with s ( · ) : ℝ 2 N → ( 0 , 1 ) and p ( · ) : ℝ 2 N → ( 1 , ∞ ) . Here, Ω ⊂ ℝ N is a bounded smooth domain with N > p(x, y)s(x, y) for any ( x , y ) ∈ Ω ¯ × Ω ¯ , μ is a positive parameter, g is a continuous and subcritical function, while variable exponent r(x) could be close to the critical exponent p s ∗ ( x ) = N p ¯ ( x ) / ( N − s ¯ ( x ) p ¯ ( x ) ) , given with p ¯ ( x ) = p ( x , x ) and s ¯ ( x ) = s ( x , x ) for x ∈ Ω ¯ . We prove the existence and asymptotic behavior of at least one non‐trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brézis and Lieb‐type lemma for fractional Sobolev spaces with variable order and variable exponent
Subject: Matrizes laplacianas
Country: Reino Unido
Editor: Wiley
Rights: Fechado
Identifier DOI: 10.1002/mma.6813
Address: https://onlinelibrary.wiley.com/doi/full/10.1002/mma.6813
Date Issue: 2021
Appears in Collections:IMECC - Artigos e Outros Documentos

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