TY - JOUR A2 - Gopal, Dhananjay AU - Ru, Yuanfang AU - Wang, Fanglei AU - Wang, Yunhai AU - An, Tianqing PY - 2018 DA - 2018/01/02 TI - On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian SP - 9857038 VL - 2018 AB - We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian Δ2u-a+bΩu2dxΔu=fx,u,u,Δu, in Ω, u=0, Δu=0, on Ω, where a, b are positive constants. We will show that there exists b>0 such that the problem has a nontrivial solution for 0<b<b through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004. SN - 2314-8896 UR - https://doi.org/10.1155/2018/9857038 DO - 10.1155/2018/9857038 JF - Journal of Function Spaces PB - Hindawi KW - ER -