文献类型：期刊文献

英文题名：On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

作者：Ru, Yuanfang Wang, Fanglei Wang, Yunhai An, Tianqing

第一作者：Ru, Yuanfang

通信作者：Wang, YH[1]

机构：[1]Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China;[2]China Pharmaceut Univ, Coll Sci, Nanjing 211198, Jiangsu, Peoples R China;[3]Guizhou Inst Technol, Sch Mech Engn, Guiyang 550003, Guizhou, Peoples R China

第一机构：Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

通信机构：corresponding author), Guizhou Inst Technol, Sch Mech Engn, Guiyang 550003, Guizhou, Peoples R China.|贵州理工学院机械工程学院;贵州理工学院;

年份：2018

卷号：2018

外文期刊名：JOURNAL OF FUNCTION SPACES

收录：;Scopus(收录号：2-s2.0-85045932790);WOS:【SCI-EXPANDED(收录号:WOS:000422840700001)】；

基金：Yunhai Wang was supported by the projects of Guizhou Provincial Science and Technology Fund (QKH-JICHU [2017], Grant no. 1408) and the doctoral starting up foundation of Guizhou Institute of Technology (Grant no. XJGC20150408). Fanglei Wang was supported by NNSF of China (no. 11501165) and the Fundamental Research Funds for the Central Universities (2015B19414).

语种：英文

摘要：We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian Delta(2)u - (a + b integral(Omega) |del u|(2)dx)Delta u = f(x,u,del u,Delta u), in Omega, u = 0, Delta u = 0, on partial derivative Omega, 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.