@article{Wu2022, 
author = {Zijian Wu and Haibo Chen},
title = {Multiple solutions for the fourth-order Kirchhoff type problems in  RN involving concave-convex nonlinearities},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {3},
pages = {830-849},
keywords = {Nehari manifold, multiple solutions, fourth-order Kirchhoff type problems, indefinite weight functions, fibering maps},
url = {https://www.sciopen.com/article/10.3934/era.2022044},
doi = {10.3934/era.2022044},
abstract = {In this paper, we study the multiplicity of solutions for the following fourth-order Kirchhoff type problem involving concave-convex nonlinearities and indefinite weight function   Δ2u−(a+b∫RN|∇u|2dx)Δu+V(x)u=λf(x)|u|q−2u+|u|p−2u,where  u∈H2(RN)(4<N<8),  λ>0,1<q<2,4<p<2∗(2∗=2N/(N−4)),  f(x) satisfy suitable conditions, and  f(x) may change sign in  RN. Using Nehari manifold and fibering maps, the existense of multiple solutions is established. Moreover, the existence of sign-changing solution is obtained for  f(x)≡0. Our results generalize some recent results in the literature.}
}