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Positive solutions of Kirchhoff type elliptic equations in R 4 with critical growth
Author(s) -
Liu Zhisu,
Guo Shangjiang,
Fang Yanqin
Publication year - 2017
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.201500358
Subject(s) - mathematics , sobolev space , lemma (botany) , critical exponent , compact space , mathematical analysis , mountain pass , nonlinear system , exponent , type (biology) , elliptic curve , term (time) , pure mathematics , geometry , physics , ecology , linguistics , philosophy , poaceae , quantum mechanics , scaling , biology
In this paper, we study the following Kirchhoff type elliptic problem with critical growth:− a + b ∫ R 4| ∇ u | 2 d x ▵ u + u = f ( u ) + β | u | 2 uinR 4 ,u ∈ H 1 ( R 4 ) , u > 0inR 4 ,where a , β > 0 , and b ≥ 0 , and the nonlinear growth term| u | 2 u reaches the Sobolev critical exponent since2 ∗ = 4 for four spatial dimensions. In a non‐radial symmetric function space, we establish a local compactness splitting lemma of critical version to investigate the existence of positive ground state solutions.