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On a p ( x ) ‐Kirchhoff equation with critical exponent and an additional nonlocal term via truncation argument
Author(s) -
Corrêa Francisco Julio S. A.,
Costa Augusto César dos Reis
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400198
Subject(s) - mathematics , bounded function , truncation (statistics) , sobolev space , exponent , critical exponent , mathematical analysis , multiplicity (mathematics) , term (time) , domain (mathematical analysis) , pure mathematics , mathematical physics , scaling , physics , geometry , quantum mechanics , statistics , philosophy , linguistics
We study existence and multiplicity of solutions of the following nonlocal p ( x ) ‐Kirchhoff equation with critical exponent, via truncation argument on the Sobolev space with variable exponent,− M ∫ Ω 1 p ( x )| ∇ u | p ( x )Δ p ( x ) u=λ f ( x , u )∫ Ω F ( x , u )r + | u | q ( x ) − 2 u ,inΩ ,u =0 ,on∂ Ω ,where Ω is a bounded smooth domain ofR N , p , q ∈ C ( Ω ¯ ) , M , f are continuous functions, 1 < p ( x ) < N , F ( x , u ) = ∫ 0 u f ( x , ξ )d ξ and λ , r > 0 are real parameter.