TY - JOUR
T1 - Existence of solutions for fourth order elliptic equations of Kirchhoff type
AU - Wang, Fanglei
AU - Avci, Mustafa
AU - An, Yukun
PY - 2014/1/1
Y1 - 2014/1/1
N2 - This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type (1){δ2u-λ(a+b∫Ω|∇;u|2dx)δu=f(x,u),inΩ,u=0,δu=0,on∂Ω, where a>0, b≥0 are constants, and λ>0 is a parameter. We will show that there exists a λ* such that (1) has nontrivial solutions for 0<λ<λ* by using the mountain pass techniques and the truncation method.
AB - This paper is concerned with the existence of nontrivial solutions for a class of fourth order elliptic equations of Kirchhoff type (1){δ2u-λ(a+b∫Ω|∇;u|2dx)δu=f(x,u),inΩ,u=0,δu=0,on∂Ω, where a>0, b≥0 are constants, and λ>0 is a parameter. We will show that there exists a λ* such that (1) has nontrivial solutions for 0<λ<λ* by using the mountain pass techniques and the truncation method.
KW - Fourth order elliptic equation
KW - Mountain pass theorem
KW - Nontrivial solutions
KW - Truncation method
UR - http://www.scopus.com/inward/record.url?scp=84883454185&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2013.07.003
DO - 10.1016/j.jmaa.2013.07.003
M3 - Journal Article
AN - SCOPUS:84883454185
SN - 0022-247X
VL - 409
SP - 140
EP - 146
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -