带有非局部项的四阶椭圆型方程组的无穷多高能量解的存在性  

High Energy solutions of Forth-Order Elliptic Systems Involving Nonlocal Term and Sign-Changing Potential

作　　者：钱雅雯 贾高[1] 

机构地区：[1]上海理工大学理学院,上海

出　　处：《应用数学进展》2019年第12期1943-1952,共10页Advances in Applied Mathematics

摘　　要：该文主要研究如下含变号位势和非局部项的四阶椭圆方程组其中Δ2=Δ(Δ)是重调和算子,V(x)∈C( ?3,?),F(x,u,v)∈C1(?3x?x?,?),V(x)为变号函数,Fu=?F/?u,Fv=?F/?v。在满足一定条件下,利用Fountain定理证明了该问题存在无穷多高能量解。This paper focus on the following forth-order elliptic equations involving non-local terms andsign-changing potentialWhere Δ2=Δ(Δ) is the biharmonic operator, V(x)∈C( ?3,?), F(x,u,v )∈C1(?3x?x?,?). V(x) is sign-changing function, Fu=?F/?u, Fv=?F/?v. Under certain conditions, it’s proved that there are infinitely many high-energy solutions to the problem using Fountain Theorem.

关 键 词：重调和 非局部项 变号位势 高能量解 

分 类 号：O17[理学—数学]