Open AccessSolutions to Kirchhoff equations with critical exponent
Author(s) -
El Miloud Hssini,
Mohammed Massar,
Najib Tsouli
Publication year - 2015
Publication title -
arab journal of mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.353
H-Index - 11
eISSN - 2588-9214
pISSN - 1319-5166
DOI - 10.1016/j.ajmsc.2015.04.001
Subject(s) - mathematics , critical exponent , exponent , mathematical analysis , mathematical physics , geometry , linguistics , philosophy , scaling
In this paper, we study the following problems {Δ2u−M(∫Ω|∇u|2dx)Δu=λf(x,u)+|u|2∗−2uinΩu=Δu=0on∂Ω, where 2∗=2NN−4 is the critical exponent. Under some conditions on M and f, we prove the existence of nontrivial solutions by using variational methods
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