四阶拟线性椭圆型方程的基态解  

Ground State Solutions for a Fourth Order Quasilinear Elliptic Equation

作　　者：胡蝶 张齐[1] Hu Die;Zhang Qi(School of Mathematics and Statistics,Central South University,Changsha,Hunan 410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《数学理论与应用》2021年第2期39-56,共18页Mathematical Theory and Applications

摘　　要：本文研究四阶拟线性椭圆型方程:{△^(2)u−△u+V(x)u−1/2u△(u^(2))=f(u),x∈R^(N),u∈H^(2)(R^(N)),其中△^(2):=△(△)为双调和算子,2<N≤6,我们证明上述方程具有Nehari-Pohozaev型基态解.This paper studies the following fourth order quasilinear elliptic equation{△^(2)u−△u+V(x)u−1/2u△(u^(2))=f(u),x∈R^(N),u∈H^(2)(R^(N)),where△^(2):=△(△)is the biharmonic operator,2<N≤6.We prove that the equation admits a ground state solution of the Nehari-Pohoz̆aev type.

关 键 词：四阶拟线性椭圆型方程 Pohozaev型基态解 变分法 

分 类 号：O175.25[理学—数学]