Solutions to Kirchhoff equations with critical exponent

Arab Journal of Mathematical Sciences

Mohammed Massar¹  El Miloud Hssini²  Najib Tsouli² 

[1] University Mohamed I, Faculty of Sciences & Techniques, Al-Hoceima, Morocco;University Mohamed I, Faculty of Sciences, Department of Mathematics, Oujda, Morocco;

关键词: Fourth-order elliptic equations;    Nonlocal problem;    Critical exponent;    Lions principle;   

DOI  :  10.1016/j.ajmsc.2015.04.001

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown